Reliable dissipative control for stochastic impulsive systems. (English) Zbl 1283.93258

Zhang, Hao; Guan, Zhi-Hong; Feng, Gang

Automatica 44, No. 4, 1004-1010 (2008).

Summary: This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly (\(Q,S,R\))-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on \(H^{\infty}\) control.

MSC:

93E03	Stochastic systems in control theory (general)
93B52	Feedback control
93E15	Stochastic stability in control theory
93D09	Robust stability

Keywords:

stochastic robust stability; Markov models; reliable dissipative control; impulsive effects

References:

[1]	Boukas, E.K.; Liu, Z.K., Robust stability and stability of Markov jump linear uncertain systems with mode-dependent time delays, Journal of optimization theory and applications, 209, 587-600, (2001) · Zbl 0988.93062
[2]	Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[3]	Gao, J.P.; Huang, B.; Wang, Z.D., LMI-based robsut \(H^\infty\) control of uncertain linear jumps systems with time-delays, Automatica, 37, 1141-1146, (2001) · Zbl 0989.93029
[4]	Guan, Z.H.; David, J.H.; Shen, X.M., On hybrid impulsive and switching systems and application to nonlinear control, IEEE transactions on automatic control, 50, 1058-1062, (2005) · Zbl 1365.93347
[5]	Hill, D.J.; Moylan, P.J., Dissipative dynamical systems: basic input-output and state properties, Journal of the franklin institute, 309, 327-357, (1980) · Zbl 0451.93007
[6]	Huang, L. (1984). Linear algebra in system and control theory (pp. 211-214). Beijing: Science Press.
[7]	Li, Z.H.; Wang, J.C.; Shao, H.H., Delay-dependent dissipative control for linear time-delay systems, Journal of the franklin institute, 39, 529-542, (2002) · Zbl 1048.93050
[8]	Maria, M.S.; David, J.H.; Aliexander, L.F., Nonlinear adaptive control of feedback passive systems, Automatica, 31, 1053-1060, (1995) · Zbl 0833.93033
[9]	Seo, C.J.; Kim, B.K., Robust and reliable \(H^\infty\) control for linear systems with parameter uncertainty and actuator failure, Automatica, 32, 465-467, (1996) · Zbl 0850.93214
[10]	Wang, Y.; Xie, L.; de Souza, C.E., Robust control of a class of uncertain nonlinear systems, Systems and control letters, 19, 139-149, (1992) · Zbl 0765.93015
[11]	Wang, Z.D.; 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, 48, 646-650, (2001) · Zbl 1023.93070
[12]	Wang, Z.D.; Huang, H.; Vnbehauen, H., Robust reliable control for a class of uncertain nonlinear state-delayed system, Automatica, 35, 936-955, (1999)
[13]	Willems, J.C., Dissipative dynamical system—part 1: general theory, Archives of the rational mechanics and analysis, 45, 321-351, (1972) · Zbl 0252.93002
[14]	Wu, M.; He, Y.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-1439, (2004) · Zbl 1059.93108
[15]	Xu, S.Y.; Chen, T.W., \(H^\infty\) output feedback control for uncertain stochastic systems with time-varying delays, Automatica, 40, 2091-2098, (2004) · Zbl 1073.93022