Exponential synchronization of delayed memristor-based neural networks with stochastic perturbation via nonlinear control

Abstract

This paper considers the exponential synchronization problem of a series of novel stochastic memristor-based neural networks (SMNNs) with time-varying delay. Firstly, under the definition of the Filippov’s solution, the stochastic perturbation and nonlinear control are considered simultaneously to form a novel SMNNs system, which is the difference from the existing models. Then, by using the Lyapunov–Krasovskii theory and the basic techniques of mathematics, several sufficient verifiable conditions are obtained to achieve the exponential stability for the error SMMNs. Moreover, a concise and unified expression form is put forward in the process of dealing with ever-changing weight matrix coefficients, so that the main conclusions can be shown in the form of linear matrix inequalities (LMIs), which makes the conditions have lower conservativeness. Finally, one illustrative example is proposed to verify the validity and the reliability of the given results.