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Dynamic output feedback ${H}_{\infty }$ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach. (English) Zbl 1111.93017
Summary: This article deals with an output feedback ${H}_{\infty }$ control problem for a class of discrete-time fuzzy dynamic systems. A full-order dynamic output feedback ${H}_{\infty }$ control design approach is developed by combining a fuzzy-basis-dependent Lyapunov function and a transformation on the controller parameters, which leads to sufficient conditions in the form of strict linear matrix inequalities (LMIs). The fuzzy-basis-dependent results are less conservative due to the generality of the fuzzy-basis-dependent Lyapunov function used which includes the fuzzy-basis-independent one as a special case. It has been shown that the underlying full-order dynamic output feedback ${H}_{\infty }$ control problem can be solved as LMI optimization problems that can be computed numerically very efficiently. Finally, two numerical examples, concerning the control of a discrete-time chaotic Lorenz system and an inverted pendulum, are given to demonstrate the applicability of the proposed approach.
MSC:
 93B36 ${H}^{\infty }$-control 93C55 Discrete-time control systems 93D30 Scalar and vector Lyapunov functions 93C42 Fuzzy control systems