Relaxed stability and stabilization conditions for a T-S fuzzy discrete system

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. (c) 2005 Elsevier B.V. All rights reserved.