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 Pj for each subregion-j is found. Then the number of Lyapunov inequalities to be satisfied by the corresponding local common matrix Pj 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.