Variance‐constrained H_∞ synchronization control of discrete time‐delayed complex dynamical networks: An intermittent pinning approach

Abstract

In this paper, the variance‐constrained H∞ synchronization control problem is investigated for a class of discrete time‐delayed complex dynamical networks. Considering the case where a dynamical network cannot achieve the synchronization by itself, the feedback controllers are added to drive the network toward a desired orbit. To further decrease both the frequency of controller update and the energy consumption, an intermittent pinning strategy is developed to control only a small part of the network nodes. The purpose of the addressed synchronization control problem is to design a set of feedback controllers such that the closed‐loop system achieves both the prescribed H∞ disturbance attenuation level and the variance constraints. By resorting to a combination of the Lyapunov stability theory and the switching system approach, a sufficient condition is obtained under which the dynamical network reaches the overall synchronization. Furthermore, the expected gains of the intermittent pinning controllers are parameterized by solving a set of linear matrix inequalities. Finally, a numerical example is exploited to verify the effectiveness of our proposed theoretical results.

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