Discrete-time memristive recurrent neural networks with time-varying delays: Exponential stability analysis

Abstract

In this paper, we study the global exponential stability problem for a class of discrete-time memristive recurrent neural networks (MRNNs) with time-varying delays. For the neural networks under consideration, the activation functions are assumed to be slope-bounded. By employing the theories of set-valued mapping, difference inclusions as well as homeomorphic mapping, the existence of the equilibrium point of the discrete-time MRNNs is first discussed. Then, by choosing an appropriate Lyapunov-Krasovskii functional, a sufficient condition is derived under which the equilibrium point of the addressed discrete-time MRNNs is globally exponentially stable. The derived condition is dependent on both the upper and lower bounds of the time-varying time delays. Furthermore, the obtained condition is expressed in terms of the linear matrix inequalities (LMIs) which can be checked numerically. Finally, a simulation example is given to show the effectiveness of the proposed stability criterion.