A relaxed stability criterion for T-S fuzzy discrete system

Stability conditions for T-S fuzzy discrete systems based on a conventional quadratic Lyapunov function or a weighting dependent Lyapunov function have been proposed in lots of literature. This paper tries to relax the conservatism of those stability conditions. By using the concept of firing rules group by each input and the examination of the maximum distance of two successive states of the system, the stability criterion can be relaxed obviously. The relaxed stability criterion give us one more chance to examine the stability of the T-S fuzzy discrete system if the common matrix P does not exist or those Lyapunov inequalities, which are derived based on the weighting dependent Lyapunov function, do not hold. An example is illustrated to show the relaxation effectiveness of the proposed stability criterion.