Discontinuous control for exponential synchronization of complex-valued stochastic multi-layer networks

Abstract

This article is concerned with the exponential synchronization issue of complex-valued stochastic multi-layer networks (CVSMLNs) via two discontinuous control approaches. At first, a new network model of complex-valued multi-layer network is built by integrating stochastic disturbances, intra-layer and inter-layer couplings. Different from previous aperiodic intermittent control (APIC) approaches, under the framework of APIC, novel impulsive feedback control (IFC) (IFC is executed at the activation time of APIC) and universal adaptive feedback control (adaptive control gain is different in different layers) are both developed to realize the exponential synchronization of CVSMLNs. Subsequently, some simple sufficient criteria are derived by virtue of Lyapunov method, graph theory and complex generalized Itô’s formula. Ultimately, the theoretical results are used in a practical complex-valued neural network and the availability of the obtained results is verified by giving some numerical examples.