Local and Global Finite-Time Synchronization of Fractional-Order Complex Dynamical Networks via Hybrid Impulsive Control

This article focuses on achieving the finite-time synchronization (FTS) for fractional complex dynamical networks (FCDNs) using hybrid impulsive control. Initially, a novel framework for local FTS is developed, building upon the relaxed inequality ${}_{t_{k}}^{C}D_{t}^{\alpha }V(t) \le \chi V(t) - \eta $ . To expand the attraction domain within the local FTS framework, a piecewise fractional-order differential inequality based on impulsive control systems is proposed. Subsequently, a new hybrid control strategy is designed by integrating a simple feedback controller with an impulsive controller involving a finite number of impulses, which can be accurately calculated using the proposed impulsive degree. Additionally, a set of local/global FTS criteria is formulated, and the settling time can be explicitly estimated. Lastly, an illustrative example is presented to demonstrate the effectiveness of the derived results.