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Zbl 1082.93035
Wang, Wen-June; Sun, Chung-Hsun
Relaxed stability and stabilization conditions for a T-S fuzzy discrete system. (English)
[J] Fuzzy Sets Syst. 156, No. 2, 208-225 (2005). ISSN 0165-0114

Summary: It is known that the stability condition of a T-S fuzzy discrete system depends on the existence of the common matrix {\bf P} which satisfies all Lyapunov inequalities. In general, the common matrix {\bf P} can be found by means of linear matrix inequalities (LMI) method. However, if the number of rules of a fuzzy system is large, the common matrix {\bf P} may not exist or may not be found even using LMI. Therefore, in this paper, the state space is divided into several subregions and the local common matrix ${\bold P}_{j}$ for each subregion-$j$ is found. Then the number of Lyapunov inequalities to be satisfied by the corresponding local common matrix ${\bold P}_{j}$ becomes much fewer such that the stability condition of the fuzzy system is more relaxed. The similar derivation is also extended to solve the stabilization problem of the T-S fuzzy discrete system with parallel distributed compensation.

MSC 2000:: *93C42 Fuzzy control
93D05 Lyapunov and other classical stabilities of control systems
93D15 Stabilization of systems by feedback

Keywords: fuzzy control; stability; T-S model; relaxed conditions

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