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Relaxed stability and stabilization conditions for a T-S fuzzy discrete system. (English) Zbl 1082.93035
Summary: It is known that the stability condition of a T-S fuzzy discrete system depends on the existence of the common matrix P which satisfies all Lyapunov inequalities. In general, the common matrix 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 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 𝐏 j for each subregion-j is found. Then the number of Lyapunov inequalities to be satisfied by the corresponding local common matrix 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:
93C42Fuzzy control systems
93D05Lyapunov and other classical stabilities of control systems
93D15Stabilization of systems by feedback