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
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