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

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_iS to satisfy r² Lyapunov inequalities. The aim of this paper is to reduce the Lyapunov inequalities which should be satisfied with positive matrices P_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.