A weighting dependent Lyapunov function based relaxed stability criterion for T-S fuzzy discrete systems

Abstract

A weighting dependent Lyapunov function based stability criterion for T-S fuzzy discrete systems has been studied in lots of literature. That is to find out r (number of rules) symmetric positive matrices P/sub iS/ to satisfy r/sup 2/ Lyapunov inequalities. The aim of this paper is to reduce the Lyapunov inequalities which should be satisfied with positive matrices P/sub iS/ then the conservatism of the stability conditions would be relaxed. From the viewpoint of the group of firing rules and the maximum distance between two successive states of the system, a new relaxed stability criterion based on the weighting dependent Lyapunov function is proposed. Finally, an example is illustrated to show the relaxation effectiveness of the proposed stability criterion.