Less conservative stability criteria for neural networks with discrete and distributed delays using a delay-partitioning approach

Abstract

This paper is focused on the stability analysis of neural networks (NNs) with discrete and distributed delays. The novelty of this paper lies in the consideration of a new integral inequality proved to be less conservative than the celebrated Jensen׳s inequality and takes fully the relationship between the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities (LMIs) into account. Based on this new integral inequality approach (IIA), an appropriate Lyapunov–Krasovskii functional is constructed and showed to have a great potential efficience in practice. Besides, by employing a delay decomposition approach which gives enough thought to information of the delayed plant states, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are derived. Four numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method.