Partial Identification of Coupled Matrices for Stochastic Hybrid Multi-Layer Delayed Networks

Abstract

This paper focuses on partial identification problems of coupled matrices for stochastic hybrid multi-layer delayed networks with inter-layer and intra-layer couplings and Markovian switching. The main approach is to combine Lyapunov method, Kirchhoff’s matrix-tree theorem and stochastic analysis. By pinning control technique, partial identification criterion is got. As a special case, the whole identification criterion is also derived. At last, three numerical examples of classical Lü and Lorenz systems are provided to demonstrate the validity of the presented results. Especially the impact of Markovian switching on partial topology identification is discussed. Note to Practitioners—This paper was motivated by existing results on synchronization of multi-layer complex network with stochastic perturbation. The existing results mainly focus on exponential synchronization or asymptotic synchronization based on known coupled matrices of networks. In this paper, the coupled matrices are unknown, the drive-response systems can achieve the partial synchronization with probability one via pinning controller. Furthermore, combining with stochastic version of the LaSalle theorem, the partial identification of coupled matrices criterion has been obtained. It should be noted that the Markovian switching and time delay in this work play an important role in the identification.