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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:
 93C42 Fuzzy control systems 93D05 Lyapunov and other classical stabilities of control systems 93D15 Stabilization of systems by feedback
##### Keywords:
fuzzy control; stability; T-S model; relaxed conditions
##### Software:
LMI toolbox; LMI Control Toolbox