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Imperfect Premise Matching based Fuzzy Control with Passive Constraints for Discrete Time-Delay Multiplicative Noised Stochastic Nonlinear Systems

Cheung-Chieh Ku, Wen-Jer Chang*, Chun-Hung Lin, and Yao-Chung Chang
International Journal of Control, Automation, and Systems, vol. 11, no. 3, pp.614-623, 2013

Abstract : This paper investigates a fuzzy controller design method for discrete-time nonlinear stochastic time-delay systems which are presented by the Takagi-Sugeno (T-S) fuzzy model with multiplicative noises. Utilizing the proposed design method, the fuzzy controller can be carried out via not only state feedback scheme but also output feedback scheme. Both of them are accomplished by the concept of imperfect premise matching (IPM). For discussing the stabilization problem, the Lyapunov-Krasovskii function and passivity theory are applied to derive the sufficient conditions. Moreover, the discrete Jensen inequality is employed to decrease the conservatism of the proposed method. Finally, a numerical example for the control of a nonlinear time-delay pendulum system is provided to show the effectiveness and usefulness of the proposed design method.

Keyword : Imperfect premise matching, multiplicative noises, passivity theory and discrete Jensen inequality, Takagi-Sugeno fuzzy models.

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