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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 141))

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Abstract

In many applications one assumes that the future state of the dynamical system is determined solely by the present state of the system and is independent of the past state information.

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References

  1. J. Hale, Theory of Functional Differential Equations (Academic, New York, 1977)

    Book  MATH  Google Scholar 

  2. N.N. Krasovskii, Stability of Motion (Stanford University Press, Stanford, 1963)

    MATH  Google Scholar 

  3. K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhuser, Boston, 2003)

    Book  MATH  Google Scholar 

  4. J.E. Marshall, Control of Time-Delay System (Peter Peregrinus, Cambridge, 1979)

    MATH  Google Scholar 

  5. J.P. Richard, Time-delay systems: An overview of some recent advances and open problems. Automatica 39, 1667–1694 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Xu, J. Lam, A survey of linear matrix inequalities in stability analysis of delay systems. Int. J. Syst. Sci. 39, 1095–1113 (2008)

    Article  MATH  Google Scholar 

  7. N. Olgac, R. Sipahi, An exact method for the stability analysis of time-delayed linear time-invariant systems. IEEE Trans. Autom. Control 47, 793–797 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Sipahi, S. Niculescu, C.T. Abdallah, W. Michiels, K. Gu, Stability and stabilization of systems with time-delay. IEEE Control Syst. Mag. 31(1), 38–65 (2011)

    Article  MathSciNet  Google Scholar 

  9. W. Michiels, “Stability and stabilization of time-delay systems.” PhD thesis, Belgium, 2002

    Google Scholar 

  10. W. Michiels, K. Engelborghs, P. Vansevenant, D. Roose, Continuous pole-placement method of delay equations. Automatica 38, 747–761 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Michiels, T. Vyhlidal, An eigen value based appraoch for the stabilization of linear time-delay systems of neutral type. Automatica 41, 991–998 (2005)

    Article  MATH  Google Scholar 

  12. J.S. Luo, A. Johnson, P.P.J. van den Bosch, Delay-independent robust stability of uncertain linear system. Syst. Control Lett. 24, 33–39 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. M.S. Mahmoud, N.F. Al-muthairi, Quadratic stabilization of continuous time system with the state delay and norm bounded uncertainties. IEEE Trans. Autom. Control 39, 2135–2139 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Phoojaruenchanachai, K. Furuta, Memoryless stabilization of uncertain linear system including time-varying sate delay. IEEE Trans. Autom. Control 37, 1022–1026 (1992)

    Article  MATH  Google Scholar 

  15. J.C. Shen, B.S. Chen, F.C. Kung, Memoryless stabilization of uncertain dynamic delay system: Ricatti equation approach. IEEE Trans. Autom. Control 36, 638–640 (1991)

    Article  Google Scholar 

  16. E.I. Verriest, M.K.H. Fan, J. Kullstam, Frequency domain robust stability criteria for linear delay systems, in Proceedings of 32nd IEEE Conference on Decision and Control, 1993, pp. 3473–3478

    Google Scholar 

  17. T. Mori, H. Kokame, Stability of \(\dot{x}(t)=\text{A}\) \(x(t)+\text{ B }\) \(x(t-\tau )\). IEEE Trans. Autom. Control 34, 460–462 (1989)

    Google Scholar 

  18. K. Gu, S.I. Niculescu, Additional dynamics in transformed time-dealy systems. IEEE Trans. Autom. Control 45, 572–575 (2000)

    Article  MATH  Google Scholar 

  19. M.S. Mahmoud, Robust Control and Filtering of Time-Delay Systems (Marcel Dekker, Cambridge, 2000)

    MATH  Google Scholar 

  20. M.S. Mahmoud, Delay-dependent robust stability and stabilization of uncertain linear delay system:a linear matrix inequality approach. IEEE Trans. Autom. Control 42, 1144–1148 (1997)

    Article  MathSciNet  Google Scholar 

  21. M.S. Mahmoud, “Delay-dependent stability and state feedback stabilization criterion for linear time delay system,” in International Conference on Modeling and Simulation, Coimbator, Vol. 2, 2007), pp. 963–968

    Google Scholar 

  22. S.G. Chen, A.G. Ulsoy, Y. Koren, Computational stability analysis of chatter in turning discrete delay and norm-bounded uncertainty. J. Manuf. Sci. Eng. 119, 457–460 (1997)

    Article  Google Scholar 

  23. M.N.A. Parlakci, Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time-delay system. Int. J. Robust Nonlinear Control 16, 599–636 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Bellen, Z. Marino, Numerical Methods for Delay-Differential Equations (Oxford University Press, London, 2005)

    MATH  Google Scholar 

  25. S. Boyd, L. Ghaoui, E. Feron, V. Balakrishnan, LMI in Systems and Control Theory (SIAM, Philadelphia, 1994)

    MATH  Google Scholar 

  26. C. Scherer, S. Weiland, “Lecture notes for DISC course on linear matrix inequalities in control,” http://www.er.ele.tue.nl/SWeiland/lmi99.htm, 1999

  27. P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control Toolbox Users Guide (Mathworks, Cambridge, 1995)

    Google Scholar 

  28. T. Coleman, M. Branch, A. Grace, Optimization Toolbox for Use with MATLAB (Mathworks, Natick, 1999)

    Google Scholar 

  29. K. Zhou, J.C. Doyel, K. Glover, Robust and Optimal Control. Prentice Hall, 1995

    Google Scholar 

  30. V.B. Kolmanovoskii, On the liapunov-krasovskii functionals for stability analysis for linear time-delay systems. Int. J. Control 72, 374–384 (1999)

    Article  Google Scholar 

  31. J.H. Kim, Delay and its time-derivative robust stability of time delayed linear systems with uncertainty. IEEE Trans. Autom. Control 46, 789–792 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  32. J.H. Kim, Delay-dependent stability and \(H_{\infty }\) control: Constant and time-varying delays. Int. J. Control 76, 48–60 (2003)

    Article  MathSciNet  Google Scholar 

  33. T.J. Su, C. Huang, Robust stability of delay dependence for linear uncertain systems. IEEE Trans. Autom. Control 37, 1656–1659 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  34. P.L. Liu, T.J. Su, Robust stability of interval time-delay systems with delay-dependence. Syst. Control Lett. 33, 231–239 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  35. E. Fridamn, U. Shaked, A descriptor system approach to \(H_{\infty }\) control of linear time-delay systems. IEEE Trans. Autom. Control 47, 253–270 (2002)

    Article  MathSciNet  Google Scholar 

  36. P. Park, A delay dependent stability criterion for systems with uncertain time-invariant delays. IEEE Trans. Autom. Control 44, 876–877 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  37. X. Li, C.E. de Souza, Criteria for robust stability and stabilization of uncertain linear systems with state delays. Automatica 33, 1657–1662 (1997)

    Article  MathSciNet  Google Scholar 

  38. Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, Delay-dependent robust stabilization of uncertain state delayed system. Int. J. Control 74, 1447–1455 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  39. H. Gao, J. Lam, C. Wang, Y. Wang, Delay-dependent output feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Appl. 151, 691–698 (2004)

    Article  Google Scholar 

  40. X.M. Zhang, M. Wu, J.H. She, Y. He, Delay-dependent stabilisation of linear systems with time-varying state and input delays. Automatica 41, 1405–1412 (2005)

    Article  MATH  Google Scholar 

  41. V. Suplin, E. Fridman, U. Shaked, \(H_{\infty }\) control of linear uncertain time-delay systems-a projection approach. IEEE Trans. Autom. Control 31, 680–685 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  42. H.J. Cho, J.H. Park, Novel delay-dependent robust stability criterion of delayed cellular neural networks. Chaos, Solitons Fractals 32, 1194–1200 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  43. E. Fridman, New-lyapunov-krasovskii functional for stability of linear retarded and neutral type. Syst. Control Lett. 43, 309–319 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  44. E. Fridman, M. Dambrine, Control under quantization, saturation and delay:an \(\text{ LMI }\) appraoch. Automatica 45, 2258–2264 (2009)

    Article  MATH  Google Scholar 

  45. E. Fridman, A. Pila, U. Shaked, Regional stabilization and \(H_\infty \) control of time-delay systems with saturating actuators. Int. J. Robust Nonlinear Control 13, 885–907 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  46. E. Fridman, U. Shaked, An improved stabilization method for linear time-delay system. IEEE Trans. Autom. Control 47, 1931–1937 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  47. E. Fridman, U. Shaked, Descriptor discretized lyapunov functional method: analysis and design. IEEE Trans. Autom. control 51, 890–897 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  48. Y. Sun, L. Wang, G. Xie, Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. Appl. Math. Comput. 180, 428–435 (2006)

    MathSciNet  MATH  Google Scholar 

  49. E. Fridman, U. Shaked, X. Li, Robust \(H_{\infty }\) filtering of linear systems with time-varying delay. IEEE Trans. Autom. Control 48, 159–165 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  50. Y. He, M. Wu, J.H. She, G. Liu, Delay-dependent robust stability criteria for uncertain neutral system with mixed delays. Syst. Control Lett. 51, 57–65 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  51. Y. He, W. Min, J.H. She, G.P. Liu, Parameter dependent lyapunov functional for stability of time delay systems with polytopic uncertainties. Automatica 492, 828–832 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  52. Y. He, Q.-G. Wang, L. Xie, C. Lin, Further improvements of free weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52, 293–299 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  53. Y. He, Q.G. Wang, C. Lin, M. Wu, Delay-range-dependent stability for systems with time-varying delay. Automatica 43, 371–376 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  54. R. Dey, G. Ray, S. Ghosh, A. Rakshit, Stability analysis for contious system with additive time-varying delays: a less conservative result. Appl. Math. Comput. 215, 3740–3745 (2010)

    MathSciNet  MATH  Google Scholar 

  55. R. Dey, S. Ghosh, G. Ray, A. Rakshit, State feedback stabilization of uncertain linear time-delay systems: a nonlinear matrix inequality appraoch. Numer. Linear Algebra Appl. 18(3), 351–361 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  56. J. Lam, H. Gao, C. Wang, Stability analysis for continuous system with two additive time-varying delay components. Syst. Control Lett. 56, 16–24 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  57. S. Xu, J. Lam, D.W.C. Ho, Y. Zou, Delay-dependent exponential satbility for a class of neural networks with time-delay. J. Comput. Appl. Math. 183, 16–28 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  58. S. Xu, J. Lam, X. Mao, Y. Zou, A new \(\text{ LMI }\) condition for delay-dependent robust stability of stochastic time-delay systems. Asian J. Control 7, 419–423 (2005)

    Article  MathSciNet  Google Scholar 

  59. L. Zhang, E.-K. Boukas, A. Haider, Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica 44, 2691–2695 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  60. J.H. Park, O. Kwon, On new stability criterion for delay-differential systems of neutral type. Appl. Math. Comput. 162, 627–637 (2005)

    MathSciNet  MATH  Google Scholar 

  61. O.M. Kwon, J.H. Park, Guaranteed cost control for uncertain large-sacle systems with time-delays via delayed feedback. Chaos, Solitons Fractals 27, 800–812 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  62. H. Shao, Improved delay-dependent stability criteria for systems with a delay varying in range. Automatica 44, 3215–3218 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  63. H. Shao, New delay-dependent stability criteria for systems with interval delay. Automatica 45, 744–749 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  64. W.H. Chen, W.X. Zheng, Delay-dependent robust stabilisation for uncertain neutral systems with distributed delays. Automatica 43, 95–104 (2007)

    Article  MATH  Google Scholar 

  65. M. Wu, Y. He, J.H. She, New delay-dependent stability criteria and stabilizing method for neutral system. IEEE Trans. Autom. Control 49, 2266–2271 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  66. S. Niculescu, A.T. Neto, J.M. Dion, L. Dugard, “Roust stability and stabilization of uncertain linear systems with state delay: multiple delay case \(\text{(I) }\),” in IFAC Symposium on Robust Control Design, 1994

    Google Scholar 

  67. Y.S. Lee, Y.S. Moon, W.H. Kwoon, K.H. Lee, in “Delay-Dependent Robust \({H_{\infty }}\) Control of Uncertain System with Time-Varying State Delay,” 2001, pp. 3208–3213

    Google Scholar 

  68. G.J. Hua, P.M. Frank, C.F. Lin, Robust \(H_{\infty }\) state feedback control for linear systems with state delay and parameter uncertainty. Automatica 32, 1183–1185 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  69. M.S. Mahmoud, M. Zribi, \(H_{\infty }\) controllers for linearized time-delay systems using \(\text{ LMI }\). J. Optim. Theory Appl. 100, 89–112 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  70. M. Zribi, M.S. Mahmoud, M. Karkoub, T.T. Lie, \(H_{\infty }\) controller for linearized time-delay power system. IEE Proc. Gener. Transm. Distrib. 147, 401–403 (2000)

    Article  Google Scholar 

  71. X. Li, E. Fridman, U. Shaked, Robust \(H_{\infty }\) control of distributed delay systems with application to combustion control. IEEE Trans. Autom. Control 46, 1930–1933 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  72. X. Yu, K. Tomsovic, Application of linear matrix inequalities for load frequency control with communication delay. IEEE Trans. Power Syst. 19, 1508–1515 (2004)

    Article  Google Scholar 

  73. Y. Zhao, Y. Ou, L. Zhang, H. Gao, \(H_{\infty }\) control of uncertain seat suspension systems subject to input delay and actuator saturation, in IEEE \(48{th}\) Conference on Decision and Control, vol. 14, 2009, pp. 5164–5169

    Google Scholar 

  74. G.J. Li, T.T. Lie, C.B. Soh, G.H. Yang, Decentralized \(H_{\infty }\) control for power system stability enhancement. Electr. Power Energy Syst. 20, 453–464 (1998)

    Article  Google Scholar 

  75. J.M.G.D. Silva, A. Seuret, E. Fridman, J.P. Richard, Stabilization of neutral systems with saturating control inputs. Int. J. Syst. Sci. (2010). https://doi.org/10.1080/00207720903353575

  76. J.M.G.D. Silva, A. Seuret, E. Fridman, J.P. Richard, Control Systems with Actuator Saturation: Analysis and Design (Birkhauser, Boston, 2001)

    Google Scholar 

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Dey, R., Ray, G., Balas, V.E. (2018). Introduction. In: Stability and Stabilization of Linear and Fuzzy Time-Delay Systems. Intelligent Systems Reference Library, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-70149-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-70149-3_1

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