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Switched Time-Delay Systems pp 297–349Cite as

Switched Decentralized Control

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Abstract

There are real-world systems consisting of coupled units or subsystems that directly interact with each other in a simple and predictable fashion to serve a common pool of objectives. When viewed as a whole, the resulting overall system often displays rich and complex behavior. Typical examples are found in electric power systems with strong interactions, water networks, which are widely distributed in space, traffic systems with many external signal or large-space flexible structures, to name a few, which are often termed large-scale or interconnected systems. It becomes increasingly evidently that the underlying notions of interconnected systems manifest the complexity as an essential and dominating problem in systems theory and practice and that the many associated problems cannot be tackled using one-shot approaches. Recent research investigations have revealed [8] that the crucial need for improved methodologies relies on dividing the analysis and synthesis of the overall system into independent or almost independent subproblems, searches for new ideas of dealing with the incomplete information about the system, for treating with the uncertainties, and for dealing with delays. System complexity frequently leads to severe difficulties that are encountered in the tasks of analyzing, designing, and implementing appropriate control methods.

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References

  1. Mahmoud, M. S., Delay-Dependent \(\mathcal{H}_{2}\) Filtering of a Class of Switched Discrete-Time State-Delay Systems, J. Signal Process., vol. 88, no. 11, 2008, pp. 2709–2719.

    MATH  Google Scholar 

  2. Mignone, D. G. F. Trecate and M. Morari, Stability and Stabilization of Piecewise Affine and Hybrid Systems: An LMI Approach, Proceedings of the 39th IEEE CDC, Sydney, Australia, 2000, pp. 504–509.

    Google Scholar 

  3. Bakule, L. and M. de la Sen, Decentralized Stabilization of Uncertain Symmetric Composite Systems, Proc. IFAC/IFORS/IMACS Symp. Large Scale Syst.: Theory Appl., vol. 1, 1998, pp. 265–270.

    Google Scholar 

  4. Mahmoud, M. S., Linear Hybrid Systems with Time-Varying Delays: \(\mathcal{H}_{\infty}\) Stabilization Schemes, Int. J. Syst. Contr. Commun., vol. 1, no. 2, 2008, pp. 147–169.

    Google Scholar 

  5. Boukas, E. K. and M. S. Mahmoud, A Practical Approach to Control of Nonlinear Discrete-Time State-Delay Systems, Optimal Contr. Appl. Methods, vol. 10, 2007, pp. 1–21.

    MathSciNet  Google Scholar 

  6. Mahmoud, M. S. and Yuanqing Xia, Robust Filter Design for Piecewise Discrete-Time Systems with Time-Varying Delays, Int. J. Robust Nonlinear Contr., vol. 20, no. 3, 2010, pp. 540–560.

    Google Scholar 

  7. Pettersson, S. and B. Lennartson, Controller Design of Hybrid Systems, in Lecture Notes in Computer Science, vol. 1201, Springer, Berlin, 1997, pp. 240–254.

    Google Scholar 

  8. Pettersson, S. and B. Lennartson, Hybrid System Stability and Robustness Verification Using Linear Matrix Inequalities, Int. J. Contr., vol. 75, 2002, pp. 1335–1355.

    MathSciNet  MATH  Google Scholar 

  9. Ohtake, H., K. Tanaka and H. O. Wang, Switching Fuzzy Controller Design Based on Switching Lyapunov Function for a Class of Nonlinear Systems, IEEE Trans. Syst. Man Cybern.-Part B, vol. 36, 2006, pp. 13–23.

    Google Scholar 

  10. Branicky, M., Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems, IEEE Trans. Automat. Contr., vol. 43, no. 4, 1998, pp. 475–582.

    MathSciNet  MATH  Google Scholar 

  11. Mahmoud, M. S., M. N. Nounou and H. N. Nounou, Analysis and Synthesis of Uncertain Switched Discrete-Time Systems, IMA J. Math. Contr. Inf., vol. 24, 2007, pp. 245–257.

    MathSciNet  MATH  Google Scholar 

  12. Liberzon, D. and A. Morse, Basic Problems in Stability and Design of Switched Systems, IEEE Contr. Syst. Mag., vol. 19, no. 5, 1999, pp. 59–70.

    Google Scholar 

  13. Mahmoud, M. S., Abdulla Ismail and F. M. AL-Sunni, A Parameterization Approach to Stability and Feedback Stabilization of Linear Time-Delay Systems, Proc. IME Part I- J. Syst. Contr. Eng., vol. 223, no. 17, 2009, pp. 929–939.

    Google Scholar 

  14. Ji, Z. and L. Wang, Robust \(\mathcal{H}_{\infty}\) Control and Quadratic Stabilization of Uncertain Switched Linear Systems, Proceedings of the American Control Conference, Portland, OR, 2004, pp. 4543–4548.

    Google Scholar 

  15. Liu, F. and S. Y. Zhang, Robust Decentralized Output Feedback Control of Similar Composite System with Uncertainties Unknown, Proceedings of the American Control Conference, vol. 6, Boston, MA, 1999, pp. 3838–3842.

    Google Scholar 

  16. Mahmoud, M. S., Y. Shi and F. M. AL-Sunni, Dissipativity Analysis and Synthesis of a Class of Nonlinear Systems with Time-Varying Delays, J. Franklin Inst., vol. 346, 2009, pp. 570–592.

    MathSciNet  MATH  Google Scholar 

  17. Mahmoud, M. S. and A. Y. AlRayyah, Adaptive Control of Systems with Mismatched Nonlinearities and Time-Varying Delays using State-Measurements, IET Contr. Theory Appl., vol. 4, no. 1, 2010, pp. 27–36.

    MathSciNet  Google Scholar 

  18. Pettit, N. B. L. and P. E. Wellstead, Analysing Piecewise Linear Dynamical Systems, IEEE Contr. Syst. Mag., vol. 15, 1995, pp. 43–50.

    Google Scholar 

  19. Mahmoud, M. S. and H. E. Emara-Shabaik, New \(\mathcal{H}_{2}\) Filter for Uncertain Singular Systems using Strict LMIs, J. Circuits, Syst. Signal Process., vol. 28, no. 5, 2009, pp. 665–677.

    MathSciNet  MATH  Google Scholar 

  20. Persis, C. D., R. D. Santis and A. S. Morse, Supervisory Control with State-Dependent Dwell-Time Logic and Constraints, Automatica, vol. 40, 2004, pp. 269–275.

    MATH  Google Scholar 

  21. Mahmoud, M. S. and N. B. Almutairi, Improved Resilient Filtering for Linear Discrete-Time Systems, J. Math Contr. Sci. Appl., vol. 1, no. 2, 2007, pp. 351–364.

    Google Scholar 

  22. Palhares, R. M., P. Peres and C. de Souza, Robust \(\mathcal{H}_{\infty}\) Filtering for Linear Continuous-Time Uncertain Systems with Multiple Delays: An LMI Approach, Proceedings of the 3rd IFAC Conference Robust Control Design, Prague, Check Republic, 2000.

    Google Scholar 

  23. Milot, J., M. J. Rodriguez and J. B. Serodes Song, Contribution of Neural Networks for Modeling Trihalomethanes Occurrence in Drinking Water, J. Water Resour. Plann. Manage., vol. 128, 2002, pp. 370–376.

    Google Scholar 

  24. Bakule, L., Decentralized Control: An Overview, Annu. Rev. Contr., vol. 32, 2008, pp. 87–98.

    Google Scholar 

  25. Mahmoud, M. S., A. W. Saif and P. Shi, Stabilization of Linear Switched Delay Systems: \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Methods, J. Optim. Theory Appl., vol. 142, no. 3, July 2009, pp. 583–607.

    MathSciNet  MATH  Google Scholar 

  26. Hovd, M. and S. Skogestad, Control of Symmetrically Interconnected Plants, Automatica, vol. 30, 1994, pp. 957–973.

    MathSciNet  MATH  Google Scholar 

  27. Yuanqing Xia, Y., Zheng Zhu and M. S. Mahmoud, H2 control for Networked Control Systems with Markovian Data Losses and Delay, Proceedings of the 2nd International Symposium on Intelligent Informatics (ISII 2009), QinHuangDao, China, September 13–15, 2009, and in ICIC Express Letters (ICIC-EL).

    Google Scholar 

  28. Pagilla, P. R., Robust Decentralized Control of Large-Scale Interconnected Systems: General Interconnections, Proceedings of American Control Conference, San Diego, CA, 1999, pp. 4527–4531.

    Google Scholar 

  29. Mahmoud, M. S. and Yuanqing Xia, Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays, J. Optim. Theory Appl., vol. 143, no. 2, 2009, pp. 329–355.

    MathSciNet  MATH  Google Scholar 

  30. Parlakci, M. N. A., Robust Stability of Uncertain Systems with Time-Varying State-Delayed Systems, IEE Proc.- Contr. Theory Appl., vol. 153, no. 4, 2006, pp. 469–477.

    MathSciNet  Google Scholar 

  31. Saif, A. W., M. S. Mahmoud and Y. Shi, A Parameterized Delay-Dependent Approach to Control of Uncertain Switched Discrete-Time Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 5, no. 10, 2009, pp. 1071–1082.

    Google Scholar 

  32. Benzaouia, A., E. De Santis, P. Caravani and N. Daraoui, Constrained Control of Switching Systems: A Positive Invariant Approach, Int. J. Contr., vol. 80, 2007, 1379–1387.

    MATH  Google Scholar 

  33. Gahinet, P., A. Nemirovski, A. L. Laub and M. Chilali, LMI Control Toolbox, The Math Works, Boston, MA, 1995.

    Google Scholar 

  34. Leite, V. J. and M. F. Miranda, Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach, Math Probl. Eng., 2008, vol. 2008, pp. 1–15.

    MathSciNet  Google Scholar 

  35. Pettersson, S., Synthesis of Switched Linear Systems, Proceedings of the 42nd IEEE Conference on Decision and Control, Boston, MA, 2003, pp. 5283–5288.

    Google Scholar 

  36. Mahmoud, M. S., E. K. Boukas and P. Shi, Resilient Feedback Stabilization of Discrete-Time Systems with Delays, IMA J. Math. Contr. Inf., vol. 25, no. 2, 2008, pp. 141–156.

    MathSciNet  MATH  Google Scholar 

  37. Moon, Y. S., P. Park, W. H. Kwon and Y. S. Lee, Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems, Int. J. Contr., vol. 74, no. 14, 2001, pp. 1447–1455.

    MathSciNet  MATH  Google Scholar 

  38. Nesic, D. and D. Liberzon, A Unified Framework for Design and Analysis of Networked and Quantized Control Systems, IEEE Trans. Automat. Contr., vol. 54, 2009, pp. 732–747.

    MathSciNet  Google Scholar 

  39. Mahmoud, M. S., Stabilization of Time-Delay Systems by PID Controllers, Proceedings of the 6th International Multi-Conference on Systems, Signals and Devices (SSD’09), Djerba-Tunisia, March 23–26, 2009, Paper # 1569171107.

    Google Scholar 

  40. Boyd, S., L. El. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, {SIAM Stud. Appl. Math}., Philadelphia, 1994.

    Google Scholar 

  41. . Bakule, L., Complexity-Reduced Guaranteed Cost Control Design for Delayed Uncertain Symmetrically Connected Systems, Proc. Am. Contr. Conf., 2005, pp. 2590–2595.

    Google Scholar 

  42. Pettersson, S. and B. Lennartson, Stabilization of Hybrid Systems Using a Min-Projection Strategy, Proceedings of the 2001 American Control Conference, Arlington, VA, 2001, pp. 223–228.

    Google Scholar 

  43. Mahmoud, M. S., State-Feedback Stabilization of Linear Systems with Input and State Delays, Proc. IME Part I- J. Syst. Contr. Eng., vol. 233, no. 14, June 2009, pp. 557–565. DOI: 10.1243/09596518JSCE723.

    Google Scholar 

  44. Niculescu, S.-I., J.-M. Dion and L. Dugard, Robust Stabilization for Uncertain Time delay Systems Containing Saturating Actuators, IEEE Trans. Automat. Contr., vol. 41, 1996, pp. 742–747.

    MathSciNet  MATH  Google Scholar 

  45. Mahmoud, M. S. and N. B. Almutairi, Stability and Implementable \(\mathcal{H}_{\infty}\) Filters for Singular Systems with Nonlinear Perturbations, Nonlinear Dyn., vol. 57, no. 6, 2009, pp. 401–410.

    MathSciNet  MATH  Google Scholar 

  46. Nian, X. and R. Li, Robust Stability of Uncertain Large-Scale Systems with Time-Delay, Int. J. Syst. Sci., vol. 32, 2001, pp. 541–544.

    MathSciNet  MATH  Google Scholar 

  47. Singh, T. and S. R. Vadali, Robust Time-Delay Control of Multimode Systems, Int. J. Contr., vol. 62, no. 2, 1995, pp. 1319–1339.

    MathSciNet  MATH  Google Scholar 

  48. Miranda, M. F. and V. J. S. Leite, Convex Analysis and Synthesis for Uncertain Discrete-Time Systems with Time-Varying State-Delay, Proceedings of American Control Conference, Seattle, Washington, June 11–13, 2008, pp. 4910–4915.

    Google Scholar 

  49. Mahmoud, M. S., P. Shi and Y. Shi, Simultaneous \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control of Uncertain Jumping Systems with Functional Time-Delays, Int. J. Robust Nonlinear Contr., vol. 18, no. 3, 2008, pp. 296–318.

    MathSciNet  Google Scholar 

  50. Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Mixed \(\mathcal{H}_{2}-\mathcal{H}_{\infty}\) Control of Uncertain Jumping Time-Delay Systems, J. Franklin Inst., vol. 345, no. 5, 2008, pp. 536–552.

    MathSciNet  MATH  Google Scholar 

  51. Mahmoud, M. S., M. F. Hassan and M. G. Darwish, Large Scale Control Systems: Theories and Techniques, Marcel Dekker, New York, NY, 1985.

    MATH  Google Scholar 

  52. Nesic, D. and A. R. Teel, Input-to-State Stability of Networked Control Systems, Automatica, vol. 40, 2004, pp. 2121–2128.

    MathSciNet  MATH  Google Scholar 

  53. Mahmoud, M. S., Y. Shi and F. M. AL-Sunni, Robust \(\mathcal{H}_{2}\) Output Feedback Control for a Class of Time-Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 4, no. 12, 2008, pp. 3247–3257.

    Google Scholar 

  54. Montagner, V. F., V. J. S. Leite, S. Tarbouriech and P. L. D. Peres, Stability and Stabilizability of Discrete-Time Switched Linear Systems with State-Delay, Proceedings of American Control Conference, Portland, OR, 2005, pp. 3806–3811.

    Google Scholar 

  55. Oucheriah, S., Decentralized Stabilization of Large-Scale Systems with Multiple Delays in the Interconnection, Int. J. Contr., vol. 73, 2000, pp. 1213–1223.

    MathSciNet  MATH  Google Scholar 

  56. Mahmoud, M. S. and Abdulla Ismail, Resilient Control of Nonlinear Discrete-Time State-Delay Systems, Appl. Math Comput., vol. 206, no. 2, 2008, pp. 561–569.

    MathSciNet  MATH  Google Scholar 

  57. Mahmoud, M. S. and Awatef Kamal M Ali, A Robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Control Approach to Uncertain Systems with Time-varying Delays, Proc. IME Part I- J Syst. Contr. Eng., vol. 223, no. 14, 2009, pp. 507–520.

    Google Scholar 

  58. Palhares, R. M. and P. L. D. Peres, Robust Filtering with Guaranteed Energy-to-Peak Performance- An LMI Approach, Automatica, vol. 36, 2000, pp. 851–855.

    MathSciNet  MATH  Google Scholar 

  59. Meyer, C., S. Schroder and R. W. De Doncker, Solid-State Circuits Breakers and Current Limiters for Medium-Voltage Systems having Distributed Power Systems, IEEE Trans. Power Electron., vol. 19, 2004, pp. 1333–1340.

    Google Scholar 

  60. Park, P. G. and J.W. Ko, Stability and Robust Stability for Systems with a Time-Varying Delay, Automatica, vol. 43, 2007, pp. 1855–1858.

    MathSciNet  MATH  Google Scholar 

  61. Martinez, L. A. M. and C. H. Moog, New Insights on the Analysis of Nonlinear Time-Delay Systems: Application to The Triangular Equivalence, Syst. Contr. Lett., vol. 56, 2007, pp. 133–140.

    MATH  Google Scholar 

  62. Zhang, L., P. Shi and E. K. Boukas, \(\mathcal{H}_{\infty}\) Output-Feedback Control for Switched Linear Discrete-Time Systems with Time-Varying Delays, Int. J. Contr., vol. 80, 2007, pp. 1354–1365.

    MATH  Google Scholar 

  63. Mahmoud, M. S., Robust Control and Filtering for Time-Delay Systems, Marcel-Dekker, New-York, NY, 2000.

    MATH  Google Scholar 

  64. Mahmoud, M. S., Improved Stability and Stabilization Approach to Linear Interconnected Time-Delay Systems, Optimal Contr. Appl. Methods, vol. 31, no. 3, 2010, pp. 81–92.

    MATH  Google Scholar 

  65. Palhares, R. M., C. D. Campos, P. Y. Ekel, M. C. R. Leles and M. F. S. V. DAngelo, Delay-Dependent Robust \(\mathcal{H}_{\infty}\) Control of Uncertain Linear Systems with Lumped Delays, IEE Proc. Contr. Theory Appl., vol. 153, 2005, pp. 27–33.

    Google Scholar 

  66. Mahmoud, M. S., E. K. Boukas and P. Shi, Robust Adaptive Control of Uncertain Discrete-Time State-Delay Systems, Comput. Math Appl., vol. 55, no. 11, 2008, pp. 2887–2902.

    MathSciNet  MATH  Google Scholar 

  67. Montestruque, L. A. and P. J. Antsaklis, On the Model-based Control of Networked Systems, Automatica, vol. 39, 2003, pp. 1837–1843.

    MathSciNet  MATH  Google Scholar 

  68. Morse, A. S., (Editor), Control using Logic-Based Switching, Springer, New York, NY, 1996.

    Google Scholar 

  69. Michel, A., Recent Trends in the Stability Analysis of Hybrid Dynamical Systems, IEEE Trans. Circuits Syst.-Part I, 46, 1999, pp. 120–134.

    MATH  Google Scholar 

  70. Niculescu, S.-I., On Delay-Dependent Stability Under Model Transformations of Some Neutral Linear Systems, Int. J. Contr., vol. 74, pp. 609–617.

    Google Scholar 

  71. Bakule, L. and J. Lunze, Decentralized Design of Feedback Control for Large-Scale Systems, Kybernetika, vol. 24, 1988, pp. 1–100.

    MathSciNet  Google Scholar 

  72. Niculescu, S.-I., Delay Effects on Stability: A Robust Control Approach, Springer, Berlin, 2001.

    MATH  Google Scholar 

  73. Petersen, I. R., A Stabilization Algorithm for a Class of Uncertain Linear Systems, Syst. Contr. Lett., vol. 8, 1987, pp. 351–357.

    MATH  Google Scholar 

  74. Park, J.-H., A New Delay-dependent Criterion for Neutral Systems with Multiple Delays, J. Comput. Appl. Math., vol. 136, 2001, pp. 177–184.

    MathSciNet  MATH  Google Scholar 

  75. Mukaidani, H., An LMI Approach to Guaranteed Cost Control for Uncertain Time-Delay Systems, IEEE Trans. Circuits Syst.-I, vol. 50, 2003, pp. 795–800.

    MathSciNet  Google Scholar 

  76. Mahmoud, M. S. and A. Y. AlRayyah, Efficient Parameterization to Stability and Feedback Synthesis of Linear Time-Delay Systems, IET Contr. Theory Appl., vol. 3, no. 8, 2009, pp. 1107–1118.

    MathSciNet  Google Scholar 

  77. Nagpal, K. M. and P. P. Khargonekar, Filtering and Smoothing in \(\mathcal{H}_{\infty}\) Setting, IEEE Trans. Automat. Contr., vol. 36, 1991, pp. 152–166.

    MathSciNet  MATH  Google Scholar 

  78. Mancilla-Aguilar, J. L. and R. A. Garcia, A Converse Lyapunov Theorem for Nonlinear Switched Systems, Syst. Contr. Lett., vol. 41, no. 1, 2000, pp. 67–71.

    MathSciNet  MATH  Google Scholar 

  79. Molchanov A. P. and E. Pyatnitskiy, Criteria of Asymptotic Stability of Differential and Difference Inclusions Encountered in Control Theory, Syst. Contr. Lett., vol. 13, 1989, pp. 59–64.

    MathSciNet  MATH  Google Scholar 

  80. Hassan, M. F., M. S. Mahmoud and M. I. Younis, A Dynamic Leontief Modeling Approach to Management for Optimal Utilization in Water Resources Systems, IEEE Trans. Syst. Man Cybern., vol. SMC-11, 1981, pp. 552–558.

    Google Scholar 

  81. Siljak, D. D., Decentralized Control of Complex Systems, Academic, New York, NY, 1991.

    Google Scholar 

  82. Myshkis, A., Introduction to the Theory and Applications of Functional Differential Equations, Kluwer, The Netherlands, 1999.

    MATH  Google Scholar 

  83. Montagner, V. F., V. J. S. Leite, R. C. L. F. Oliveira and P. L. D. Peres, State-Feedback Control of Switched Linear Systems: An LMI Approach, J. Comput. Appl. Math., vol. 194, 2006, pp. 192–206.

    MathSciNet  MATH  Google Scholar 

  84. Song, S. H. and J. K. Kim, \(\mathcal{H}_{\infty}\) Control of Discrete-Time Linear Systems with Norm-Bounded Uncertainties and Time-Delay in State, Automatica, vol. 34, 1998, pp. 137–139.

    MathSciNet  MATH  Google Scholar 

  85. Daafouz, J., P. Riedinger and C. Lung, Stability Analysis and Control Synthesis for Switched Systems: A Hybrid Lyapunov Function Approach, IEEE Trans. Automat. Contr., vol. 47, 2002, pp. 1883–1887.

    Google Scholar 

  86. Petersen, I. R. and D. C. McFarlane, Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems, IEEE Trans. Automat. Contr., vol. 39, 1994, pp. 1971–1977.

    MathSciNet  MATH  Google Scholar 

  87. Park, P., A Delay-Dependent Stability Criterion for Systems with Uncertain Time-Invariant Systems, IEEE Trans. Automat. Contr., vol. 44, no. 4, 1999, pp. 876–879.

    MATH  Google Scholar 

  88. Sun, Z. and S. S. Ge, Switched Linear Systems, Springer, London, 2005.

    MATH  Google Scholar 

  89. De Oliveita, M. C., J. C. Geromel and J. Bernussou, Extended \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Norm Characterizations and Controller Parameterizations for Discrete-Time Systems, Int. J. Contr., vol. 75, 2002, pp. 666–679.

    Google Scholar 

  90. Mahmoud, M. S. and N. B. Almutairi, Decentralized Stabilization of Interconnected Systems with Time-Varying Delays, Eur. J. Contr., vol. 15, no. 6, 2009, pp. 624–633.

    MathSciNet  MATH  Google Scholar 

  91. Mahmoud, M. S. and N. B. Almutairi, Improved Resilient Filtering for Linear Discrete-Time Systems, J. Math. Contr. Sci. Appl., vol. 1, no. 2, 2007, pp. 351–364.

    Google Scholar 

  92. Mahmoud, M. S., A. W. Saif and P. Shi, Stabilization of Linear Switched Delay Systems: \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Methods, J. Optim. Theory Appl., vol. 142, no. 3, 2009, pp. 583–607.

    MathSciNet  MATH  Google Scholar 

  93. Narendra, K. S. and J. Balakrishnan, A common Lyapunov Function for Stable LTI Systems with Commuting A-Matrices, IEEE Trans. Automat. Contr., vol. 39, no. 12, 1994, pp. 2469–2471.

    MathSciNet  MATH  Google Scholar 

  94. Mahmoud, M. S., Generalized \(\mathcal{H}_{2}\) Control of Switched Discrete-Time with Unknown Delays, Appl. Math Comput., vol. 311, no. 1, 2009, pp. 33–44.

    Google Scholar 

  95. Mahmoud, M. S. and S. El-Ferik, New Stability and Stabilization Methods for Nonlinear Systems with Time-Varying Delays, Optimal Contr. Appl. Methods, vol. 31, no. 2, 2010, pp. 273–287.

    MathSciNet  MATH  Google Scholar 

  96. McClamroch, N. H. and I. Kolmanvsky, Performance Benefits of Hybrid Control Design for Linear and Nonlinear Systems, Proc. IEEE, vol. 88, 2000, pp. 1083–1096.

    Google Scholar 

  97. Mahmoud, M. S., Delay-Dependent Dissipativity of Singular Time-Delay Systems, IMA J. Math. Contr. Inf., vol. 26, no. 1, 2009, pp. 45–58.

    MATH  Google Scholar 

  98. Mahmoud, M. S., Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays, J. Optim. Theory Appl., vol. 143, no. 5, 2009, pp. 497–518.

    MathSciNet  MATH  Google Scholar 

  99. Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Dissipativity Results for Linear Singular Time-Delay Systems, Int. J. Innovative Comput. Inf. Contr., vol. 4, no. 11, 2008, pp. 2833–2845.

    Google Scholar 

  100. Mahmoud, M. S., P. Shi and Y. Shi, Simultaneous \(\mathcal{H}_{2}/\mathcal{H}_{\infty}\) Control of Uncertain Jumping Systems with Functional Time-Delays, Int. J. Robust Nonlinear Contr., vol. 18, no. 3, 2008, pp. 296–318.

    MathSciNet  Google Scholar 

  101. Cao, Y. Y. and P. M. Frank, Analysis and Synthesis of Nonlinear Time-Delay Systems via Fuzzy Control Approach, IEEE Trans. Fuzzy Syst., vol. 8, no. 2, 2000, pp. 200–211.

    Google Scholar 

  102. Koutsoukos, X. D. and P. J. Antsaklis, Design of Stabilizing Switching Control Laws for Discrete- and Continuous-Time Linear Systems Using Piecewise-Linear Lyapunov Functions, Int. J. Contr., vol. 75, 2002, pp. 932–945.

    MathSciNet  MATH  Google Scholar 

  103. Mahmoud, M. S., Switched Discrete-Time with Time-Varying Delays: A Generalized \(\mathcal{H}_{2}\) Approach, Comput. Math Appl., vol. 57, no. 1, 2009, pp. 79–95.

    MathSciNet  MATH  Google Scholar 

  104. Palhares, R. M. and P. L. D. Peres, Robust \(\mathcal{H}_{\infty}\) Filtering Design with Pole Placement Constraint via LMIs, J. Optim. Theory Appl., vol. 102, 1999, pp. 239–261.

    MathSciNet  MATH  Google Scholar 

  105. Montestruque, L. A. and P. J. Antsaklis, Stability of Model-based Networked Control Systems with Time-Varying Transmission Times. IEEE Trans. Automat. Contr., vol. 49, no. 9, pp. 1562–1573.

    Google Scholar 

  106. Palhares, R. M., C. D. Campos, P. Y. Ekel, M. C. R. Leles and M. F. S. V. DAngelo, Delay-Dependent Robust \(\mathcal{H}_{\infty}\) Control of Uncertain Linear Systems with Time-Varying Delays, Comput. Math. Appl., vol. 50, 2005, pp. 13–32.

    MathSciNet  MATH  Google Scholar 

  107. DeCarlo, R., M. Branicky, S. Pettersson and B. Lennartson, Perspectives and Results on the Stability and Stabilizability of Hybrid Systems, Proc. IEEE, vol. 88, 2000, pp. 1069–1082.

    Google Scholar 

  108. Mahmoud, M. S., New Exponentially-Convergent State Estimation Method for Delayed Neural Networks, Neurocomputing, vol. 72, no. 16–18, 2009, pp. 3935–3942.

    Google Scholar 

  109. Mahmoud, M. S. and S. J. Saleh, Regulation of Water Quality Standards in Streams by Decentralized Control, Int. J. Contr., vol. 41, 1985, pp. 525–540.

    MathSciNet  MATH  Google Scholar 

  110. Mahmoud, M. S., Stabilization of Linear Time-Delay Systems by Three-Term Controllers, Proceedings of the 3rd International Multi-Conference on Systems and Control (MSC 2009), Saint Petersburg, Russia, July 8–10, 2009, pp. 296–301.

    Google Scholar 

  111. Mahmoud, M. S. and Yuanqing Xia, Design of Reduced-Order \(\mathcal{L}_{2}-\mathcal{L}_{\infty}\) Filter for Singular for Discrete-Time Systems Using Strict LMIs, IET Contr. Theory Appl., vol. 4, no. 3, 2010, pp 509–519.

    Google Scholar 

  112. Mahmoud, M. S., F. M. AL-Sunni and Y. Shi, Switched Discrete-Time Delay Systems: Delay-Dependent Analysis and Synthesis, J. Circuits, Syst. Signal Process., vol. 28, no. 5, 2009, pp. 735–761.

    MathSciNet  MATH  Google Scholar 

  113. Overstreet, J. W. and A. Tzes, An Internet-Based Real-Time Control Engineering Laboratory, IEEE Contr. Syst. Mag., vol. 19, 1999, pp. 320–326.

    Google Scholar 

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  1. Department of Systems Engineering, King Fahd University of Petroleum and Minerals (KFUPM), 31261, Dhahran, Saudi Arabia

    Magdi S. Mahmoud

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Mahmoud, M.S. (2010). Switched Decentralized Control. In: Switched Time-Delay Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6394-9_10

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