Robust stability of mixed Cohen–Grossberg neural networks with discontinuous activation functions

The purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.

Based on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.

It turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.