New global exponential stability result to a general Cohen–Grossberg neural networks with multiple delays

Abstract

In this paper, we first discuss the existence of an equilibrium point to a general Cohen–Grossberg neural networks with multiple delays by means of using degree theory and linear matrix inequality (LMI) technique. Then by applying the existence result of an equilibrium point, linear matrix inequality technique and constructing a Lyapunov functional, we study the global exponential stability of equilibrium solution to the Cohen–Grossberg neural networks. Compared with known results, our results of global exponential stability of equilibrium point are new. In our results, the hypothesis for differentiability in existing papers on the behaved functions is removed and the hypotheses for boundedness and monotonicity in existing papers on the activation functions are also removed.