Novel LMI-Based Condition on Global Asymptotic Stability for a Class of Cohen–Grossberg BAM Networks With Extended Activation Functions

This paper is concerned with global asymptotic stability of a class of Cohen-Grossberg bidirectional associative memory (BAM) neural networks with delays. Under the assumptions that the activation functions only satisfy the so-called extended global Lipschitz condition and the behaved functions only satisfy global Lipschitz condition, we apply linear matrix inequality (LMI) method and homeomorphism theory to propose a new LMI-based sufficient condition for global asymptotic stability of the concerned neural networks. In our results, the extended global Lipschitz condition on the activation functions is less conservative than the assumptions for boundedness and monotonicity and is weaker than the assumption for the general global Lipschitz condition, the global Lipschitz condition on the behaved functions is also less conservative than the assumptions for monotonicity and differentiability in existing papers.