Skip to main content
SpringerLink
Log in

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

  • Reviews
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to asymptotic stabilization of the equilibria of nonlinear dynamic systems using the dynamic output feedbacks, that is, the feedbacks in the estimate of system state made by the asymptotic observer. Presented were the basic methods of constructing the asymptotic observers for the nonlinear dynamic systems with control and the approaches to system stabilization using the system state estimate made by the observer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Vidyasagar, M., On the Stabilization of Nonlinear Systems Using State Detection, IEEE Trans. Automat. Control, 1980, vol. 25, pp. 504–509.

    Google Scholar 

  2. Byrnes, C.I. and Isidori, A., New Results and Counterexamples in Nonlinear Feedback Stabilization, Syst. Control Lett., 1989, no. 12, pp. 437–442.

  3. Tsinias, J. and Kalouptsidis, N., Output Feedback Stabilization, IEEE Trans. Automat. Control, 1990, vol. 35, no.8, pp. 951–954.

    Google Scholar 

  4. Tsinias, J., Optimal Controllers and Output Feedback Stabilization, Syst. Contr. Lett., 1990, no. 15, pp. 277–284.

  5. Tsinias, J., A Generalization of Vidyasagar’s Theorem on Stabilizability Using State Detection, Syst. Contr. Lett., 1991, no.17, pp. 37–42.

  6. Tsinias, J., A Theorem on Global Stabilization of Nonlinear Systems by Linear Feedback, Syst. Contr. Lett., 1991, no. 17, pp. 357–362.

  7. Marino, R. and Tomei, P., Dynamic Output Feedback Linearization and Global Stabilization, Syst. Contr. Lett., 1991, no. 17, pp. 115–121.

  8. Byrnes, C.I. and Isidori, A., Asymptotic Stabilization of Minimum Phase Nonlinear Systems, IEEE Trans. Automat. Control, 1991, vol. 36, no.10, pp. 1122–1137.

    Google Scholar 

  9. Kanellakopoulos, I., Kokotovic, P.V., and Morse, A.S., A Toolkit for Nonlinear Feedback Design, Syst. Contr. Lett., 1992, no. 18, pp. 83–92.

  10. Praly, L., Lyapunov Design of a Dynamic Output Feedback for Systems Linear in Their Unmeasured State Components, Proc. 2nd IFAC Nonlinear Control Syst. Design Sympos. Nolcos’92, Bordeaux, 1992, pp. 31–36.

  11. Tornambe, A., Output Feedback Stabilization of a Class of Non-minimum Phase Nonlinear Systems, Syst. Contr. Lett., 1992, no. 19, pp. 193–204.

  12. Esfandiari, F. and Khalil, H.K., Output Feedback Stabilization of Fully Linearizable Systems, Int. J. Control, 1992, vol. 56, pp. 1007–1037.

    Google Scholar 

  13. Gauthier, J.P. and Kupka, I., A Separation Principle for Bilinear Systems with Dissipative Draft, IEEE Trans. Automat. Control, 1992, vol. 37, no.12, pp. 1970–1974.

    Google Scholar 

  14. Tsinias, J., Sontag’s ‘Input to State Stability Condition’ and Global Stabilization Using State Detection, Syst. Contr. Lett., 1993, no. 20, pp. 219–226.

  15. Ailon, A. and Ortega, R., An Observer-based Set-point Controller for Robot Manipulators with Flexible Joints, Syst. Contr. Lett., 1993, no. 21, pp. 329–335.

  16. Marino, R. and Tomei, P., Global Adaptive Output-feedback Control of Nonlinear Systems. I. Linear Parametrization, IEEE Trans. Automat. Control, 1993, vol. 38, no.1, pp. 17–32.

    Google Scholar 

  17. Marino, R. and Tomei, P., Global Adaptive Output-feedback Control of Nonlinear Systems. II. Nonlinear Parametrization, IEEE Trans. Automat. Control, 1993, vol. 38, no.1, pp. 33–48.

    Google Scholar 

  18. Khalil, H.K. and Esfandiari, F., Semiglobal Stabilization of a Class of Nonlinear Systems Using Output Feedback, IEEE Trans. Automat. Control, 1993, vol. 38, no.9, pp. 1412–1415.

    Google Scholar 

  19. Praly, L. and Jiang, Z.P., Stabilization by Output Feedback for Systems with ISS Inverse Dynamics, Syst. Contr. Lett., 1993, no. 21, pp. 19–33.

  20. Berghuis, H. and Nijmeijer, H., Global Regulation of Robots Using Only Position Measurements, Syst. Contr. Lett., 1993, no. 21, pp. 289–293.

  21. Berghuis, H. and Nijmeijer, H., A Passivity Approach to Controller-Observer Design for Robots, IEEE Trans. Robotics Automat, 1993, vol. 9, no.6, pp. 740–754.

    Google Scholar 

  22. Pomet, J.B., Hirschorn, R.M., and Cebuhar, W.A., Dynamic Output Feedback Regulation for a Class of Nonlinear Systems, Math. Control, Signals Syst., 1993, no. 6, pp. 106–124.

  23. Teel, A. and Praly, L., On Output Feedback Stabilization for Systems with IIS Inverse Dynamics and Uncertainties, Proc. 32nd IEEE Conf. Decision and Control, San Antonio, Texas, 1993, pp. 1942–1947.

  24. Teel, A. and Praly, L., Global Stabilizability and Observability Imply Semi-global Stabilizability by Output Feedback, Syst. Contr. Lett., 1994, no. 22, pp. 313–325.

  25. Mazenc, F., Praly, L., and Dayawansa, W.P., Global Stabilization by Output Feedback: Examples and Counterexamples, Syst. Contr. Lett., 1994, no. 23, pp. 119–125.

  26. Lin, W., Bounded Smooth State Feedback and a Global Separation Principle for Non-Affine Nonlinear Systemsw, Syst. Contr. Lett., 1995, no. 26, pp. 41–53.

  27. Teel, A. and Praly, L., Tools for Semiglobal Stabilization by Partial State and Output Feedback, SIAM J. Control Optimiz, 1995, vol. 33, no.5, pp. 1443–1488.

    Google Scholar 

  28. Lin, W., Input Saturation and Global Stabilization of Nonlinear Systems via State and Output Feedback, IEEE Trans. Automat. Control, 1995, vol. 40, pp. 776–782.

    Google Scholar 

  29. Lin, Z. and Saberi, A., Robust Semi-Global Stabilization of Minimum-Phase Input-Output Linearizable Systems via Partial State and Output Feedback, IEEE Trans. Automat. Control, 1995, vol. 40, no.6, pp. 1029–1041.

    Google Scholar 

  30. Kucera, V. and De Souza, C., A Necessary and Sufficient Condition for Output Feedback Stabilizability, Automatica, 1995, vol. 31, no.9, pp. 1357–1359.

    Google Scholar 

  31. Nicosia, S. and Tomei, P., A Global Output Feedback Controller for Flexible Joint Robots, Automatica, 1995, vol. 31, no.10, pp. 1465–1469.

    Google Scholar 

  32. Freeman, R., Global Internal Stabilizability Does Not Imply Global External Stabilizability for Small Sensor Disturbances, IEEE Trans. Automat. Control, 1995, vol. 40, no.12, pp. 2119–2122.

    Google Scholar 

  33. Druzhinina, M.V., Nikiforov, V.O., and Fradkov, A.L., Output-based Methods of Adaptive Control of Nonlinear Plants, Avtom. Telemekh., 1996, no. 2, pp. 3–33.

  34. Jankovic, M., Adaptive Output Feedback Control of Nonlinear Feedback Linearizable Systems, Int. J. Adaptive Control Signal Proc., 1996, vol. 10, pp. 1–18.

    Google Scholar 

  35. Jouan, P. and Gauthier, J.P., Finite Singularities of Nonlinear Systems, Output Stabilization, Observability and Observers, J. Dynamical Control Syst., 1996, vol. 2, no.2, pp. 255–288.

    Google Scholar 

  36. Khalil, H.K., Adaptive Output Feedback Control of Nonlinear Systems Represented by Input-Output Models, IEEE Trans. Automat. Control, 1996, vol. 41, no.2, pp. 177–188.

    Google Scholar 

  37. Battilotti, S., Global Output Regulation and Disturbance Attenuation with Global Stability via Measurement Feedback for a Class of Nonlinear Systems, IEEE Trans. Automat. Control, 1996, vol. 41, no.3, pp. 315–327.

    Google Scholar 

  38. Freeman, R. and Kokotovic, P.V., Tracking Controllers for Systems Linear in the Unmeasured States, Automatica, 1996, vol. 32, pp. 735–746.

    Google Scholar 

  39. Khalil, H.K. and Strangas, E.G., Robust Speed Control of Induction Motors Using Position and Current Measurement, IEEE Trans. Automat. Control, 1996, vol. 41, no.8, pp. 1216–1220.

    Google Scholar 

  40. Mahmoud, N.A. and Khalil, H.K., Asymptotic Regulation of Minimum Phase Nonlinear Systems Using Output Feedback, IEEE Trans. Automat. Control, 1996, vol. 41, no.10, pp. 1402–1412.

    Google Scholar 

  41. Tsinias, J., Versions of Sontag’s Input to State Stability Condition and Output Feedback Global Stabilization, J. Math. Syst., Estimation Control, 1996, vol. 6, no.1, pp. 1–17.

    Google Scholar 

  42. Battilotti, S., Lanari, L., and Ortega, R., On the Role of Passivity and Output Injection in the Output Feedback Stabilization Problem: Application to Robot Control, Eur. J. Control, 1997, vol. 3, no.3, pp. 92–103.

    Google Scholar 

  43. Jankovic, M., Adaptive Nonlinear Output Feedback Tracking with a Partial High-Gain Observer and Backstepping, IEEE Trans. Automat. Control, 1997, vol. 42, no.1, pp. 106–113.

    Google Scholar 

  44. Syrmos, V., Abdallah, C., Dorato, P., and Grigoriadis, K., Static Output Feedback—A Survey, Automatica, 1997, vol. 33, pp. 125–137.

    Google Scholar 

  45. Nikiforov, V.O., Output-based Robust Control of Linear Plant, Avtom. Telemekh., 1998, no. 9, pp. 87–99.

  46. Burdakov, S.F., Using Indirect Compensation to Design Control of the Elastic Robot under Uncertain Mathematical Model, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 1, pp. 149–155.

  47. Jiang, Z.P., A Note on Robust Adaptive Output Feedback Control, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 20–25.

  48. Battilotti, S., Semiglobal Stabilization of Uncertain Block-feedforward Systems via Measurement Feedback, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 342–347.

  49. Besancon, G., State-affine Systems and Observer-based Control, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 399–404.

  50. Isidori, A., Semiglobal Practical Stabilization of Uncertain Non-Minimum-Phase Nonlinear Systems via Output Feedback, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 643–648.

  51. Marino, R. and Tomei, P., Robust Adaptive Tracking by Measurement Feedback for a Class of Nonlinear Systems, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 673–678.

  52. Peresada, S. and Tonielli, A., Exponentially Stable Output Feedback Control of Induction Motor, Proc. 4th IFAC Nonlinear Control Syst., Design Sympos., Enschede, 1998, pp. 726–731.

  53. Robertsson, A. and Johansson, R., Nonlinear Observers and Output Feedback Control with Application to Dynamically Positioned Ships, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 818–823.

  54. Battilotti, S., A General Theorem on the Semiglobal Stabilization of Uncertain Nonlinear Systems via Measurement Feedback, Proc. 4th IFAC Nonlinear Control Syst. Design Sympos., Enschede, 1998, pp. 848–853.

  55. Battilotti, S., Robust Output Feedback Stabilization via a Small-gain Theorem, Int. J. Robust Nonlin. Control, 1998, vol. 9, pp. 211–229.

    Google Scholar 

  56. Geromel, J.C., De Souza, C., and Skelton, R.E., Static Output Feedback Controllers: Stability and Convexity, IEEE Trans. Automat. Control, 1998, vol. 43, no.1, pp. 120–125.

    Google Scholar 

  57. Ding, Z., Global Adaptive Output Feedback Stabilization for Nonlinear Systems of any Relative Degree with Unknown High-frequency Gains, IEEE Trans. Automat. Control, 1998, vol. 43, pp. 1442–1446.

    Google Scholar 

  58. Fossen, T.I. and Grovlen, A., Nonlinear Output Feedback Control of Dynamically Positioned Ships Using Vectorial Observer Backstepping, IEEE Trans. Control Syst. Tech., 1998, vol. 6, no.1, pp. 121–128.

    Google Scholar 

  59. Robertsson, A. and Johansson, R., Comments on “Nonlinear Output Feedback Control of Dynamically Positioned Ships Using Vectorial Observer Backstepping,” IEEE Trans. Control Syst. Tech., 1998, vol. 6, no.3, pp. 439–441.

    Google Scholar 

  60. Jiang, Z. and Hill, D., Passivity and Disturbance Attenuation via Output Feedback for Uncertain Nonlinear Systems, IEEE Trans. Automat. Control, 1998, vol. 43, no.7, pp. 992–997.

    Google Scholar 

  61. Besancon, G., Battilotti, S., and Lanari, L., On Output Feedback Tracking Control with Disturbance Attenuation for Euler-Lagrange Systems, Proc. 37th IEEE Conf. Decision Contr., Tampa, Florida, 1998, pp. 3139–3143.

  62. Atassi, A.N. and Khalil, H.K., A Separation Principle for the Control of a Class of Nonlinear Systems, Proc. 37th IEEE Conf. Decision Contr., Tampa, Florida, 1998, pp. 855–860.

  63. Atassi, A.N. and Khalil, H.K., A Separation Principle for the Stabilization of a Class of Nonlinear Systems, IEEE Trans. Automat. Control, 1999, vol. 44, no.9, pp. 1672–1687.

    Google Scholar 

  64. Loria, A. and Panteley, E., A Separation Principle for a Class of Euler-Lagrange Systems, in New Directions in Nonlinear Observer Design, London: Springer, 1999.

    Google Scholar 

  65. Arcak, M. and Kokotovic, P.V., Observer-based Stabilization of Systems with Monotonic Nonlinearities, Asian J. Control, 1999, vol. 1, pp. 42–48.

    Google Scholar 

  66. Robertsson, A. and Johansson, R., Observer Backstepping for a Class of Nonminimum-Phase Systems, Proc. 38th IEEE Conf. Decision Contr., Phoenix, Arizona, 1999, pp. 4866–4871.

  67. Padilla, S., Alvarez, J., and Castellanos, E., Linear Measurement Feedback Control of Nonlinear Plants, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 225–229.

  68. Tan, Y. and Kanellakopoulos, I., Adaptive Nonlinear Observer/Controller Design for Uncertain Nonlinear Systems, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 237–242.

  69. Jiang, Z.P., Nonlinear Disturbance Attenuation with Global Stability via Output Feedback, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 315–320.

  70. Chen, P., Qin, H., and Zhu, Q.M., Dynamic Output Feedback Stabilization of Partially Linear Composite Systems, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 345–350.

  71. Chen, W., Chu, X., Shi, S., and Liu, X., Robust Adaptive Output-Feedback Control of a Class of Uncertain Nonlinear Systems, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 375–380.

  72. Marino, R. and Tomei, P., Adaptive Output Feedback Tracking for a Class of Nonlinear Systems with Time-Varying Parameters, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 381–386.

  73. Johansson, R. and Robertsson, A., The Yakubovich-Kalman-Popov Lemma and Stability Analysis of Dynamic Output Feedback Systems, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 393–398.

  74. Mazenc, F. and Astolfi, A., Robust Output Feedback Stabilization of the Angular Velocity of a Rigid Body, Proc. 14th IFAC World Congr., Beijing, 1999, pp. 405–410.

  75. Zuber, I.E. and Petrova, K.Yu., Design of Controllers for a Nonstationary Model of an Autonomous Transportation Vehicle, Diff. Uravn. Protsessy Upravlen., 2000, no. 4 (http://www.neva.ru/journal).

  76. Besancon, G., Global Output Feedback Tracking Control for a Class of Lagrangian Systems, Automatica, 2000, vol. 36, pp. 1915–1921.

    Google Scholar 

  77. Besancon, G. and Hammouri, H., Some Remarks on Dynamic Output Feedback Control of Non-Uniformly Observable Systems, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  78. Aamo, O.M., Arcak, M., Fossen, T.I., and Kokotovic, P.V., Global Output Tracking Control of a Class of Euler-Lagrange Systems, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  79. Maggiore, M. and Passino, K., Robust Output Feedback Control of Incompletely Observable Nonlinear Systems without Input Dynamic Extension, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  80. Polushin, I., On the Output Feedback Control of Passive Nonlinear Systems with Input Perturbations, Proc. 39th IEEE Conf. Decision Contr., Sydney, 2000.

  81. Astolfi, A. and Colaneri, P., Static Output Feedback Stabilization of Linear and Nonlinear Systems, Proc. 39th IEEE Conf. Decision Contr., Sydney, 2000.

  82. Praly, L. and Kanellakopoulos, I., Output Feedback Asymptotic Stabilization for Triangular Systems Linear in the Unmeasured State Components, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  83. Arcak, M. and Kokotovic, P.V., Robust Output-feedback Design Using a New Class of Nonlinear Observers, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  84. Jiang, Z.P. and Arcak, M., Robust Global Stabilization with Input Unmodeled Dynamics: An ISS Small-gain Approach, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  85. Maggiore, M. and Passino, K., Output Feedback Control of Stabilizable and Incompletely Observable Systems: Theory, Proc. Am. Control Conf., Chicago, 2000, pp. 3641–3645.

  86. Isidori, A., A Tool for Semiglobal Stabilization of Uncertain Non-Minimum-Phase Nonlinear Systems via Output Feedback, IEEE Trans. Automat. Control, 2000, vol. 45, no.10, pp. 1817–1827.

    Google Scholar 

  87. Isidori, A., Teel, A., and Praly, L., A Note on the Problem of Semiglobal Practical Stabilization of Uncertain Nonlinear Systems via Dynamic Output Feedback, Syst. Contr. Lett., 2000, no. 39, pp. 165–171.

  88. Shim, H. and Seo, J.H., Nonlinear Output Feedback Stabilization on a Bounded Region of Attraction, Int. J. Control, 2000, vol. 73, no.5, pp. 416–426.

    Google Scholar 

  89. Arcak, M. and Kokotovic, P.V., Observer-based Control of Systems with Slope-restricted Nonlinearities, Proc. Am. Control Conf., Arlington, 2001, pp. 384–389.

  90. Arcak, M. and Kokotovic, P.V., Observer-based Control of Systems with Slope-restricted Nonlinearities, IEEE Trans. Automat. Control, 2001, vol. 46, no.7, pp. 1146–1150.

    Google Scholar 

  91. Arcak, M. and Kokotovic, P.V., Nonlinear Observers: A Circle Criterion Design and Robustness Analysis, Automatica, 2001, vol. 37, pp. 1923–1930.

    Google Scholar 

  92. Besancon, G., A Note on Constrained Stabilization for Nonlinear Systems in Feedback Form, Proc. 5th IFAC Nonlinear Control Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 289–293.

  93. Shim, H. and Teel, A., Further Results on the Nonlinear Separation Principle: The General ‘Asymptotically Controllable’ Case, Proc. 5th IFAC Nonlinear Control Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 1543–1548.

  94. Battilotti, S., Lyapunov Design of Global Measurement Feedback Controllers for Nonlinear Systems, Proc. 5th IFAC Nonlinear Control Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 1561–1565.

  95. Maggiore, M. and Passino, K., Sufficient Conditions for the Solution of the Semiglobal Output Tracking Problem Using Practical Internal Models, Proc. 5th IFAC Nonlinear Control Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 1572–1577.

  96. Johansson, R. and Robertsson, A., Observer-based Strict Positive Real (SPR) Feedback Control System Design, Proc. 5th IFAC Nonlinear Control Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 1601–1606.

  97. Chen, P., Qin, H., and Huang, J., Local Stabilization of a Class of Nonlinear Systems by Dynamic Output Feedback, Automatica, 2001, vol. 37, pp. 969–981.

    Google Scholar 

  98. Lin, W. and Qian, C., Semi-Global Robust Stabilization of MIMO Nonlinear Systems by Partial State and Dynamic Output Feedback, Automatica, 2001, vol. 37, pp. 1093–1101.

    Google Scholar 

  99. Golubev, A.E., Krishchenko, A.P., and Tkachev, S.B., Separation Principle for Affine Systems, Diff. Uravn., 2001, vol. 37, no.11, pp. 1468–1475.

    Google Scholar 

  100. Serrani, A., Towards Universal Nonlinear Output Regulation, Proc. 40th IEEE Conf. Decision Contr., Orlando, Florida, 2001, pp. 59–64.

  101. Battilotti, S., New Results in the Global Stabilization of Nonlinear Systems via Measurement Feedback with Application to Nonholonomic Systems, Proc. 40th IEEE Conf. Decision Contr., Orlando, Florida, 2001, pp. 1360–1365.

  102. Praly, L., Asymptotic Stabilization via Output Feedback for Lower Triangular Systems with Output Dependent Incremental Rate, Proc. 40th IEEE Conf. Decision Contr., Orlando, Florida, 2001, pp. 3808–3813.

  103. Besancon, G. and Hammouri, H., A Semi-global Output Feedback Stabilization Scheme for a Class of Non Uniformly Observable Systems, Prepr. 15th IFAC World Congress, Barcelona, 2002.

  104. Besancon, G., Battilotti, S., and Lanari, L., A New Separation Result for Euler-Lagrange-Like Systems, Prepr. 15th IFAC World Congress, Barcelona, 2002.

  105. Efimov, D.V., Universal Formula for Output Asymptotic Stabilization, Prepr. 15th IFAC World Congress, Barcelona, 2002.

  106. Golubev, A.E., Krishchenko, A.P., and Tkachev, S.B., Separation Principle for a Class of Nonlinear Systems, Prepr. 15th IFAC World Congress, Barcelona, 2002.

  107. Prat, S. and Astolfi, A., Local Static Output Feedback Stabilization of a Class of Minimum-phase Nonlinear Systems, Prepr. 15th IFAC World Congress, Barcelona, 2002.

  108. Arcak, M., A Global Separation Theorem for a New Class of Nonlinear Observers, Proc. 41st IEEE Conf. Decision Contr., Las Vegas, Nevada, 2002, pp. 676–681.

  109. Qian, C. and Lin, W., Output Feedback Stabilization of Planar Systems with Uncontrollable/Unobservable Linearization, Proc. 41st IEEE Conf. Decision Contr., Las Vegas, Nevada, 2002, pp. 4324–4329.

  110. Loria, A. and Morales, J.L., A Cascaded Approach to a Nonlinear Separation Principle, Proc. 41st IEEE Conf. Decision Contr., Las Vegas, Nevada, 2002, pp. 695–700.

  111. Qian, C. and Lin, W., Stabilization of a Class of Nonlinear Systems by Linear Output Feedback, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1710–1715.

    Google Scholar 

  112. Qian, C. and Lin, W., Smooth Output Feedback Stabilization of Planar Systems without Controllable/Observable Linearization, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 2068–2073.

    Google Scholar 

  113. Johansson, R. and Robertsson, A., Observer-based Strict Positive Real (SPR) Feedback Control System Design, Automatica, 2002, vol. 38, pp. 1557–1564.

    Google Scholar 

  114. Yang, B. and Lin, W., Output Feedback Stabilization of a Class of Homogeneous and High-Order Nonlinear Systems, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 37–42.

  115. Qian, C. and Lin, W., Nonsmooth Output Feedback Stabilization and Tracking of a Class of Nonlinear Systems, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 43–48.

  116. Maithripala, D.H., Berg, J.M., and Dayawansa, W.P., Nonlinear Dynamic Output Feedback Stabilization of Electrostatically Actuated MEMS, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 61–66.

  117. Coutinho, D.F., Trofino, A., and Barbosa, K.A., Robust Linear Dynamic Output Feedback Controllers for a Class of Nonlinear Systems, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 374–379.

  118. Jiang, Z.P., Mareels, I., Hill, D.J., and Huang, J., A Unifying Framework for Global Regulation via Nonlinear Output Feedback, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 1047–1052.

  119. Praly, L. and Jiang, Z.P., On Global Output Feedback Stabilization of Uncertain Nonlinear Systems, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 1544–1549.

  120. Shiriaev, A., Johansson, R., and Robertsson, A., Sufficient Conditions for Dynamical Output Feedback Stabilization via the Circle Criterion, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 4682–4687.

  121. Do, K.D., Jiang, Z.P., and Pan, J., Global Output-feedback Tracking Control of a VTOL Aircraft, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 4914–4919.

  122. Karafyllis, I. and Kravaris, C., Robust Output Feedback Stabilization and Nonlinear Observer Design, Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 5847–5852.

  123. Davison, D.E., Hwang, E.S., and Li, X., Generalization of the Separation Principle Beyond Constant-gain State-feedback Control, Proc. Am. Control Conf., Denver, Colorado, 2003, pp. 3228–3233.

  124. Qian, C., Schrader, C.B., and Lin, W., Global Regulation of a Class of Uncertain Nonlinear Systems Using Output Feedback, Proc. Am. Control Conf., Denver, Colorado, 2003, pp. 1542–1547.

  125. Marino, R. and Tomei, P., Global Tracking for a Class of Nonlinear Systems Subject to Unknown Sinusoidal Disturbances, Proc. Eur. Control Conf., Cambridge, 2003.

  126. Liu, K.Z. and He, R., A Nonlinear Output Feedback Control Method for Magnetic Bearing Systems, Proc. Eur. Control Conf., Cambridge, 2003.

  127. Xie, C. and French, M., A Performance Comparison between Backstepping and High-gain Observer Control Designs, Proc. Eur. Control Conf., Cambridge, 2003.

  128. Zuber, I.E., Stabilization of the Nonlinear Observable Systems under Output-based Control, Vest. Leningrad. Gos. Univ., 2003, no. 1, pp. 7–19.

  129. Zuber, I.E., Design of the Output-based Terminal Control of a Nonlinear System, Diff. Uravn. Protsessy Upravlen., 2004, no. 1 (http://www.neva.ru/journal).

  130. Golubev, A.E., Global Stabilization of the Nonlinear Dynamic Systems for Exponential Estimation of the State Vector, Vest. Mosk. Gos. Tekh. Univ., Ser. “Estestvennye Nauki,” 2004, no. 2, pp. 38–60.

  131. Golubev, A., Johansson, R., Robertsson, A., and Tkachev, S., Output Tracking for a Class of Nonlinear Nonminimum-Phase Systems Using Observer Backstepping, Vest. Mosk. Gos. Tekh. Univ., 2005, pp. 63–80.

  132. Byrnes, C.I., Isidori, A., and Willems, J.C., Passivity, Feedback Equivalence and the Global Stabilization of Minimum Phase Nonlinear Systems, IEEE Trans. Automat. Control, 1991, vol. 36, no.11, pp. 1228–1240.

    Google Scholar 

  133. Fradkov, A. and Hill, D., Exponential Feedback Passivity and Stabilizability of Nonlinear Systems, Automatica, 1998, vol. 34, no.6, pp. 697–703.

    Google Scholar 

  134. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.

    Google Scholar 

  135. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer, 1979. Translated under the title, Lineinye mnogomernye sistemy upravleniya: geometricheskii podkhod, Moscow: Nauka, 1980.

    Google Scholar 

  136. Mashinostroenie. Entsiklopediya. Avtomaticheskoe Upravlenie. Teoriya (Machine Building. Encyclopedia. Automatic Control. Theory), Moscow: Mashinostroenie, 2000, vols. 1–4.

  137. Krstic, M., Kanellakopoulos, I., and Kokotovic, P.V., Nonlinear and Adaptive Control Design, New York: Wiley, 1995.

    Google Scholar 

  138. Freeman, R. and Kokotovic, P.V., Robust Nonlinear Control Design. State-space and Lyapunov Techniques, Boston: Birkhauser, 1996.

    Google Scholar 

  139. Khalil, H.K., Nonlinear Systems, New York: Prentice Hall, 1996.

    Google Scholar 

  140. Gauthier, J.P. and Bornard, G., Observability for any U(T) of a Class of Nonlinear Systems, IEEE Trans. Automat. Control, 1981, vol. 26, pp. 922–926.

    Google Scholar 

  141. Hahn, W., Stability of Motion, New York: Springer, 1967.

    Google Scholar 

  142. Isidori, A., Nonlinear Control Systems, London: Springer, 1999.

    Google Scholar 

  143. Isidori, A., Nonlinear Control Systems, London: Springer, 1995.

    Google Scholar 

  144. Gauthier, J.P., Hammouri, H., and Othman, S., A Simple Observer for Nonlinear Systems. Applications to Bioreactors, IEEE Trans. Automat. Control, 1992, vol. 37, no.6, pp. 875–880.

    Google Scholar 

  145. Gauthier, J.P. and Kupka, I., Observability and Observers for Nonlinear Systems, SIAM J. Control Optimiz., 1994, vol. 32, no.4, pp. 975–994.

    Google Scholar 

  146. Gauthier, J.P. and Kupka, I., Deterministic Observation Theory and Applications, Cambridge: Cambridge Univ. Press, 2001.

    Google Scholar 

  147. Starkov, K.E., Conditions for Uniform Observability of a Class of Polynomial Systems, Avtom. Telemekh., 1996, no. 4, pp. 38–45.

  148. Sontag, E.D., Smooth Stabilization Implies Coprime Factorization, IEEE Trans. Automat. Control, 1989, vol. 34, pp. 435–443.

    Google Scholar 

  149. Sontag, E.D., Further Facts about Input to State Stabilization, IEEE Trans. Automat. Control, 1990, vol. 35, pp. 473–477.

    Google Scholar 

  150. Krener, A.J. and Respondek, W., Nonlinear Observers with Linearizable Error Dynamics, SIAM J. Control Optim., 1985, vol. 23, no.2, pp. 197–216.

    Google Scholar 

  151. Krishchenko, A.P. and Tkachev, S.B., Nonlinear K(X)-dual Systems and Observer Design, Diff. Uravn., 1999, vol. 35, no.5, pp. 648–663.

    Google Scholar 

  152. Krener, A.J. and Isidori, A., Linearization by Output Injection and Nonlinear Observers, Syst. Contr. Lett., 1983, no. 3, pp. 47–52.

  153. Xia, X. and Gao, W., Nonlinear Observer Design by Observer Canonical Forms, Int. J. Control, 1988, vol. 47, no.4, pp. 1081–1100.

    Google Scholar 

  154. Xia, X. and Gao, W., Nonlinear Observer Design by Observer Error Linearization, SIAM J. Control Optimiz., 1989, vol. 27, no.1, pp. 199–216.

    Google Scholar 

  155. Krishchenko, A.P. and Tkachev, S.B., Nonlinear K(X)-dual Systems, Avtom. Telemekh., 1995, no. 2, pp. 21–34.

  156. Thau, F.E., Observing the State of Non-Linear Dynamic Systems, Int. J. Control, 1973, no. 17, pp. 471–479.

  157. Raghavan, S. and Hedrick, J.K., Observer Design for a Class of Nonlinear Systems, Int. J. Contr., 1994, vol. 59, no.2, pp. 515–528.

    Google Scholar 

  158. Rajamani, R., Observers for Lipschitz Nonlinear Systems IEEE Trans. Automat. Control, 1998, vol. 43, no.3, pp. 397–401.

    Google Scholar 

  159. Starkov, K.E., On the Thau Observer’s Construction for Nonlinear Systems with a Time-Varying Linearization, Proc. IASTED Int. Conf. MIC’2002, Innsbruck, 2002, pp. 392–395.

  160. Arcak, M. and Kokotovic, P.V., Nonlinear Observers: A Circle Criterion Design, Proc. 38th IEEE Conf. Decision Contr., Phoenix, Arizona, 1999, pp. 4872–4876.

  161. Tsinias, J., Observer Design for Nonlinear Systems, Syst. Contr. Lett., 1989, no. 13, pp. 135–142.

  162. Tsinias, J., Further Results on the Observer Design Problem, Syst. Contr. Lett., 1990, no. 14, pp. 411–418.

  163. Song, R.Y., Ishijima, S., and Kojima, A., Design of Nonlinear Observer by a Backstepping Approach, Electrical Eng. Japan., 1997, vol. 121, no.3, pp. 53–59.

    Google Scholar 

  164. Fossen, T.I. and Strand, J.P., Passive Nonlinear Observer Design for Ships Using Lyapunov Methods: Full-Scale Experiments with a Supply Vessel, Automatica, 1999, vol. 35, pp. 3–16.

    Google Scholar 

  165. Shim, H. and Seo, J.H., Passivity Framework for Nonlinear State Observer, Proc. Am. Control Conf., Chicago, Illinois, 2000, pp. 699–705.

  166. Shim, H. and Seo, J.H., Recursive Observer Design Beyond the Uniform Observability, Proc. 30th IEEE Conf. Decision Contr., Sydney, 2000.

  167. Krasnova, S.A., Utkin, V.A., and Mikheev, Yu.V., Cascaded Design of State Observers of the Nonlinear Multidimensional Systems, Avtom. Telemekh., 2001, no. 2, pp. 43–64.

  168. Krasnova, S.A., Decomposition State Observer Design for Nonlinear Systems, Proc. 5th IFAC Nonlinear Contr. Syst. Design Sympos., St. Petersburg, Russia, 2001, pp. 997–1002.

  169. Krasnova, S.A., Cascaded Design of State Observers of the Nonlinear Systems in the Presence of External Disturbances, Avtom. Telemekh., 2003, no. 1, pp. 31–54.

  170. Zuber, I.E., Exponentially Stable Observer for Controllable and Observable Nonlinear Systems, Vest. S.-Peterburg. Gos. Univ., 2004, vol. 1, no.2, pp. 34–38.

    Google Scholar 

  171. Arcak, M. and Kokotovic, P.V., Feasibility Conditions for Circle Criterion Designs, Syst. Contr. Lett., 2001, vol. 42, no.5, pp. 405–412.

    Google Scholar 

  172. Sontag, E.D., Remarks on Stabilization and Input-to-State Stability, Proc. IEEE Conf. Decision Contr., Tampa, Florida, 1989, pp. 1376–1378.

  173. Sontag, E.D., Input/Output and State-Space Stability, in New Trends Syst. Theory, Boston: Birkhauser, 1991.

    Google Scholar 

  174. Marino, R. and Tomei, P., Global Adaptive Observers for Nonlinear Systems via Filtered Transformations, IEEE Trans. Automat. Control, 1992, vol. 37, no.8, pp. 1239–1245.

    Google Scholar 

  175. Krasovskii, N.N., Nekotorye zadachi teorii ustoichivosti dvizheniya (Some Problems of the Motion Stability Theory), Moscow: Fizmatgiz, 1959.

    Google Scholar 

  176. Sontag, E.D. and Wang, Y., On Characterizations of Input-To-State Stability Property, Syst. Contr. Lett., 1995, no. 24, pp. 351–359.

Download references

Author information

Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    A. E. Golubev, A. P. Krishchenko & S. B. Tkachev

Authors
  1. A. E. Golubev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Krishchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. B. Tkachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 3–42.

Original Russian Text Copyright © 2005 by Golubev, Krishchenko, Tkachev.

This work was supported by the Russian Foundation for Basic Research, project no. 05-01-00840, Grant for State Support of the Leading Scientific Schools, project no. NSh-2094.2003.1, and project no. UR.03.01.141 of Section 1.2 “Russian Universities” of the Subprogram “Basic Research” of the Departmental Scientific Program “Development of the Scientific Potentialities of the Higher School” of the Federal Education Agency of the Russian Federation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golubev, A.E., Krishchenko, A.P. & Tkachev, S.B. Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer. Autom Remote Control 66, 1021–1058 (2005). https://doi.org/10.1007/s10513-005-0147-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10513-005-0147-5

Keywords

Search

Navigation