Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid control.

Abstract

This paper investigates the dynamical multisynchronization (DMS) and static multisynchronization (SMS) problems for a class of delayed coupled multistable memristive neural networks (DCMMNNs) via a novel hybrid controller which includes delayed impulsive control and state feedback control. Based on the state-space partition method and the geometrical properties of the activation function, each subnetwork has multiple locally exponential stable equilibrium states. By employing a new Halanay-type inequality and the impulsive control theory, some new linear matrix inequalities (LMIs)-based sufficient conditions are proposed. It is shown that the delayed impulsive control with suitable impulsive interval and allowable time-varying delay can still guarantee the DMS and SMS of DCMMNNs. Finally, a numerical example is presented to illustrate the effectiveness of the hybrid controller.