zbMATH — the first resource for mathematics

Fuzzy model-based control of nonlinear stochastic systems with time-delay. (English) Zbl 1239.93035
Summary: This note investigates the problems of robust stabilization and robust \(H_{\infty }\) control for a class of nonlinear stochastic delay systems – stochastic fuzzy delay systems. The purpose of the robust stochastic stabilization problem is the design of a state feedback controller such that the closed-loop system is mean-square exponentially stable for all admissible uncertainties. In the robust \(H_{\infty }\) control problem, in addition, a prescribed \(H_{\infty }\) performance is required to be archived. Sufficient conditions for the solvability of these problems are given in terms of solutions to a set of linear matrix inequalities (LMIs). The developed theory is illustrated by numerical simulation.

93B36 \(H^\infty\)-control
93C42 Fuzzy control/observation systems
93D15 Stabilization of systems by feedback
93E15 Stochastic stability in control theory
Full Text: DOI
[1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. syst. man cybern., 15, 116-132, (1985) · Zbl 0576.93021
[2] Wang, H.; Tanaka, K.; Griffin, M., An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE trans. fuzzy syst., 4, Feb., 14-23, (1996)
[3] Wang, L.X.; Medel, J.M., Fuzzy basisfunctions, universal approximation, and orthogonal least-squares learning, IEEE trans. neural netw., 3, 807-814, (1992)
[4] Tanaka, K.; Wang, H., Fuzzy control systems design and analysis, (2001), John Wiley New York
[5] Tanaka, K.; Ikeda, T.; Wang, H.O., Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE trans. fuzzy syst., 6, May, 250-265, (1998)
[6] Chen, B.S.; Tseng, C.S.; Uang, H.J., Robustness design of nonlinear dynamic systems via fuzzy linear control, IEEE trans. fuzzy syst., 7, October, 571-585, (1999)
[7] Boyd, S., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia, PA
[8] Wang, Z.; Ho, D.W.C.; Liu, X., A note on the robust stability of uncertain stochastic fuzzy systems with time-delays, IEEE trans. syst. man cybern., part A, 34, 4, 570-576, (2004)
[9] L. Hu, W. Zhao, S. Shao, Robust stochastic stabilization and robust \(H^\infty\) control for uncertain stochastic fuzzy systems, in: The 14th IEEE International Conference on Fuzzy Systems, pp. 254-259, 2005
[10] Huang, H.; Ho, D.W.C., Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay, Control theory appl., IET, 1, 4, 1075-1085, (2007)
[11] Zhang, B., Delay-dependent stabilization for stochastic fuzzy systems with time delays, Fuzzy sets and systems, 158, 2238-2250, (2007) · Zbl 1122.93051
[12] Zhang, H.; Wang, Y.; Liu, D., Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays, IEEE trans. syst. man cybern., part B, 38, 1, 126-140, (2008)
[13] Mao, X., Stochastic differential equations and applications, (1997), Chichester Horwood · Zbl 0874.60050
[14] Mao, X.; Koroleva, N.; Rodkina, A., Robust stability of uncertain stochastic differential delay equations, Syt. control lett., 35, 325-336, (1998) · Zbl 0909.93054
[15] Xu, S.; Chen, T., Robust \(H_\infty\) control for uncertain stochastic systems with state delay, IEEE trans. automat. control, 47, 2089-2094, (2002) · Zbl 1364.93755
[16] Wang, Y.; Xie, L.; De Souza, C.E., Robust control of a class of uncertain nonlinear systems, Systems control lett., 19, 139-149, (1992) · Zbl 0765.93015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.