An improved stability criterion for T-S fuzzy discrete systems via vertex expression

The stability criteria for Takagi-Sugeno (T-S) fuzzy discrete systems based on a weighting-dependent Lyapunov function have been studied in numerous literature. Most of those results need to find r (number of rules) positive matrices P_is to satisfy r² Lyapunov inequalities. This paper combines the ideas of group-fired rules, estimation of the maximum distance between two successive states of the system, and the vertex expression of any point in a region together, so that the relaxed stability that satisfies fewer Lyapunov inequalities is derived. Finally, an example is illustrated to reveal the merit of the proposed stability criterion.