Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays

Abstract

In this paper, the global asymptotic stability analysis problem is investigated for a class of delayed Generalized Bi-directional Associative Memory (GBAM) networks. The mixed time delays consist of both the discrete delays and the distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and develop some new techniques, so as to establish sufficient conditions for the delayed GBAM networks to be globally asymptotically stable. These conditions are expressed in terms of the feasibility to a couple of linear matrix inequalities (LMIs). Therefore, the global asymptotic stability of the delayed GBAM can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.