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Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching. (English) Zbl 1232.93093
Summary: This paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system. A design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures, and the dwell time approach is utilized for the stability analysis. Then the approach is extended to take into account stochastic switched systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is employed to verify the proposed method.
93E15Stochastic stability
93D15Stabilization of systems by feedback
93E03General theory of stochastic systems
93C10Nonlinear control systems
[1]Balluchi, A.; Benedetto, M. D.; Pinello, C.; Rossi, C.; Sangiovanni-Vincentelli, A.: Cut-off in engine control: a hybrid system approach, Proceedings of the 36th IEEE conference on decision and control, 4720-4725 (1997)
[2]Bishop, B. E.; Spong, M. W.: Control of redundant manipulators using logic-based switching, Proceedings of the 36th IEEE conference on decision and control 2, 16-18 (1998)
[3]Zhang, W.; Branicky, M. S.; Phillips, S. M.: Stability of networked control systems, IEEE control systems magazine 21, No. 1, 84-99 (2001)
[4]Gollu, A.; Varaiya, P. P.: Hybrid dynamical systems, Proceedings of the 28th IEEE conference on decision and control, tampa, 2708-2712 (1989)
[5]Zhao, J.; Spong, M. W.: Hybrid control for global stabilization of the cart-pendulum system, Automatica 37, 1941-1951 (2001) · Zbl 1005.93041 · doi:10.1016/S0005-1098(01)00164-9
[6]Sun, Z.; Ge, S. S.: Analysis and synthesis of switched linear control systems, Automatica 41, No. 2, 181-195 (2005) · Zbl 1074.93025 · doi:10.1016/j.automatica.2004.09.015
[7]Cheng, D.; Guo, L.; Lin, Y.; Wang, Y.: Stabilization of switched linear systems, IEEE transactions on automatic control 50, No. 5, 661-666 (2005)
[8]Sun, Z.: Combined stabilizing strategies for switched linear systems, IEEE transactions on automatic control 51, No. 4, 666-674 (2006)
[9]Lin, H.; Antsaklis, P. J.: Stability and stabilizability of switched linear systems: a survey of recent results, IEEE transactions on automatic control 54, No. 2, 308-322 (2009)
[10]Sun, Z.: A robust stabilizing law for switched linear systems, International journal of control 77, No. 4, 389-398 (2004) · Zbl 1059.93121 · doi:10.1080/00207170410001667468
[11]Liberzon, D.: Switching in systems and control, (2003)
[12]Hespanha, J. P.: Uniform stability of switched linear systems: extension of lasalle’s invariance principle, IEEE transactions on automatic control 49, No. 4, 470-482 (2004)
[13]Hespanha, J. P.; Liberzon, D.; Angeli, D.; Sontag, E. D.: Nonlinear norm-observability notions and stability of switched systems, IEEE transactions on automatic control 50, No. 2, 154-168 (2005)
[14]Xiang, Z.; Wang, R.: Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching, Applied mathematics and computation 216, No. 3, 800-811 (2010) · Zbl 1217.93046 · doi:10.1016/j.amc.2010.01.084
[15]Zhai, G.; Hu, B.; Yasuda, K.: Stability analysis of switched systems with stable and unstable subsystems: an average Dwell time approach, International journal of systems science 32, No. 8, 1055-1061 (2001) · Zbl 1022.93043 · doi:10.1080/00207720010015690
[16]Li, Q. K.; Zhao, J.; Dimirovski, G. M.: Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems, Nonlinear analysis: hybrid systems 3, No. 2, 133-142 (2009) · Zbl 1166.93325 · doi:10.1016/j.nahs.2008.11.004
[17]Chatterjee, D.; Liberzon, D.: On stability of stochastic switched systems, Proceeding of the 43rd conference on decision and control, 4125-4127 (2004)
[18]Wei, F.; Zhang, J. F.: Stability analysis and stabilization control of multi-variable switched stochastic systems, Automatica 42, No. 2, 169-176 (2006) · Zbl 1121.93370 · doi:10.1016/j.automatica.2005.08.016
[19]Wu, L.; Ho, D. W. C.; Li, C. W.: Stabilisation and performance synthesis for switched stochastic systems, IET control theory and applications 4, No. 10, 1877-1888 (2010)
[20]Yao, B.; Wang, F. Z.: LMI approach to reliable H control of linear systems, Journal of systems engineering and electronics 17, No. 2, 381-386 (2006) · Zbl 1173.93332 · doi:10.1016/S1004-4132(06)60065-0
[21]Abootalebi, A.; Hossein, N. S.; Sheikholeslam, F.: Reliable H control systems with uncertainties in all system matrices: an LMI approach, Proceedings of the 2005 IEEE conference on control applications, 28-31 (2005)
[22]Lien, C. H.; Yu, K. W.; Lin, Y. F.; Chung, Y. J.; Chung, L. Y.: Robust reliable H control for uncertain nonlinear systems via LMI approach, Applied mathematics and computation 198, No. 1, 453-462 (2008) · Zbl 1141.93322 · doi:10.1016/j.amc.2007.08.085
[23]Liu, Y. Q.; Wang, J. L.; Yang, G. H.: Reliable control of uncertain nonlinear systems, Automatica 34, No. 7, 875-879 (1998) · Zbl 0942.93007 · doi:10.1016/S0005-1098(98)00027-2
[24]Yu, L.: An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure, Applied mathematics and computation 162, No. 3, 1325-1331 (2005) · Zbl 1125.93046 · doi:10.1016/j.amc.2004.03.012
[25]Yang, G. H.; Wang, J. L.; Soh, Y. C.: Reliable guaranteed cost control for uncertain nonlinear systems, IEEE transactions on automatic control 45, No. 11, 2188-2192 (2000) · Zbl 0991.93035 · doi:10.1109/9.887682
[26]Wu, H. N.: Reliable robust H fuzzy control for uncertain nonlinear systems with Markovian jumping actuator faults, Journal of dynamic systems, measurement and control, transactions of the ASME 129, No. 3, 252-261 (2007)
[27]Xia, J.; Xu, S.; Zou, Y.: Robust reliable H control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters, Journal of control theory and applications 6, No. 4, 410-414 (2008)
[28]Zhang, H.; Guan, Z. H.; Feng, G.: Reliable dissipative control for stochastic impulsive systems, Automatica 44, No. 4, 1004-1010 (2008)
[29]Chen, W. H.; Wang, J. G.; Tang, Y. J.; Lu, X.: Robust H control of uncertain linear impulsive stochastic systems, International journal of robust and nonlinear control 18, No. 13, 1348-1371 (2008)
[30]Xia, J.; Song, B.; Lu, J.: Robust H control for stochastic time-delay systems with Markovian jump parameters via parameter-dependent Lyapunov functionals, Circuits, systems, and signal processing 27, No. 3, 331-349 (2008) · Zbl 1146.93324 · doi:10.1007/s00034-008-9017-z
[31]Greco, L.; Fontanelli, D.; Bicchi, A.: Robust almost sure stability for uncertain stochastically scheduled anytime controllers, Proceedings of mediterranean conference on control and automation, 249-254 (2008)
[32]Wang, Z.; Huang, B.; Burnham, K. J.: Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities, IEEE transactions on circuits and systems I: Fundamental theory and applications 48, No. 5, 646-650 (2001) · Zbl 1023.93070 · doi:10.1109/81.922470
[33]Zhang, A. Q.; Fang, H. J.: Robust H reliable control for uncertain singular stochastic fuzzy systems, Proceedings of the IEEE international conference on automation and logistics, 1561-1566 (2008)
[34]Wang, R.; Liu, M.; Zhao, J.: Reliable H control for a class of switched nonlinear systems with actuator failures, Nonlinear analysis: hybrid systems 1, No. 3, 317-325 (2007) · Zbl 1118.93351 · doi:10.1016/j.nahs.2006.11.002
[35]Wang, R.; Zhao, J.: Robust adaptive control for a class of uncertain switched delay systems with actuator failures, Dynamics of continuous, discrete and impulsive systems, series B: applications and algorithms 15, No. 5, 635-645 (2008) · Zbl 1155.93021
[36]Xie, G.; Wang, L.: Stabilization of switched linear systems with time-delay in detection of switching signal, Journal of mathematical analysis and applications 305, No. 6, 277-290 (2005) · Zbl 1140.93463 · doi:10.1016/j.jmaa.2004.11.043
[37]Xie, W.; Wen, C.; Li, Z.: Input-to-state stabilization of switched nonlinear systems, IEEE transactions on automatic control 46, No. 7, 1111-1116 (2001) · Zbl 1010.93089 · doi:10.1109/9.935066
[38]Ji, Z.; Guo, X.; Xu, S.; Wang, L.: Stabilization of switched linear systems with time-varying delay in switching occurrence detection, Circuits, systems and signal processing 26, No. 3, 361-367 (2007) · Zbl 1118.93044 · doi:10.1007/s00034-006-0414-x
[39]Xie, D.; Chen, X.: Observer-based switched control design for switched linear systems with time-delay in detection of switching signal, IET control theory and applications 2, No. 5, 437-445 (2008)
[40]Xiang, Z. R.; Wang, R. H.: Robust control for uncertain nonlinear switched systems with time delay under asynchronous switching, IET control theory and applications 3, No. 8, 1041-1050 (2009)
[41]Zhai, G. S.; Hu, B.; Yasuda, K.; Michel, A. N.: Disturbance attenuation properties of time-controlled switched systems, Journal of the franklin institute 338, No. 7, 765-779 (2001) · Zbl 1022.93017 · doi:10.1016/S0016-0032(01)00030-8
[42]Williams, D.: Probability with martingales, (1991)
[43]Cao, Y.; Sun, Y.; Cheng, C.: Delay dependent robust stabilization of uncertain systems with multiple state delays, IEEE transactions on automatic control 43, No. 11, 1608-1612 (1998) · Zbl 0973.93043 · doi:10.1109/9.728880
[44]Xie, L.: Output feedback H control of systems with parameter uncertainty, International journal of control 63, No. 4, 741-750 (1996) · Zbl 0841.93014 · doi:10.1080/00207179608921866