Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks

Abstract

This paper carries out an investigation into the problem of the global asymptotic stability of the class of Takagi-Sugeno (T-S) fuzzy delayed Cohen-Grossberg neural networks involving discrete time delays and employing the nondecreasing and slope-bounded activation functions. A new su¢ cient criterion for the uniqueness and global asymptotic stability of the equilibrium point for this class of fuzzy neural networks is proposed. The uniqueness of the equilibrium point is proved by using the contradiction method, and the stability of the equilibrium point is established by utilizing a novel fuzzy type Lyapunov functional. The obtained stability condition is independent of the time delay parameters and, it can be easily veri…ed by exploiting some commonly used norm properties of matrices. A constructive numerical example is also given to demonstrate the applicability of the proposed stability condition.