PD-type ℓ2 - ℓ∞ Intermittent Pinning Synchronization Control of Discrete Time-delay Nonlinear Dynamical Networks

Abstract

In this paper, the PD-type l2 - l∞ synchronization control problem is concerned for a class of discrete time-delayed nonlinear dynamical networks. A PD-type (proportional-derivative-type) pinning control protocol is proposed where only a small fraction of network nodes is controlled in order to achieve the global synchronization performance. Meanwhile, for the sake of decreasing the update frequency of the controller, the periodic intermittent control strategy is developed. The main purpose of the addressed problem is to design a PD-type intermittent pinning feedback controller such that the closed-loop system achieves both the exponential synchronization and the prescribed l2 - l∞ performance index. Subsequently, by means of the Lyapunov-Krasovskii functional method, a sufficient condition is established under which the addressed PD-type controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is given to show the applicability of the developed theoretical results.