\(H_{\infty}\) filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach. (English) Zbl 1110.93034
Summary: This paper is concerned with the \(H_{\infty }\) filtering problem for a class of discrete-time fuzzy systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the \(H_{\infty }\) sense. By using basis-dependent Lyapunov functions, sufficient conditions for the solvability of this problem are obtained. It has been shown that the \(H_{\infty }\) filtering problem can be solved as a linear matrix inequality (LMI) optimization problem. Two examples are provided to demonstrate the applicability of the proposed approach.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C55 | Discrete-time control/observation systems |
| 93D30 | Lyapunov and storage functions |
| 93B36 | \(H^\infty\)-control |
Keywords:
basis-dependent Lyapunov function; fuzzy system; \(H_{\infty}\) filtering; linear matrix inequalityReferences:
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