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 Pis 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.
IEEE Trans. Systems, Man and Cybernetics Part-B36, pp.672-678