Local and Global Finite-Time Synchronization of Fractional-Order Complex Dynamical Networks via Hybrid Impulsive Control
Chen Wei, Xiaoping Wang, Fangmin Ren, Zhigang Zeng
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{{t_{k}}}^{C}D_{t}^{{\alpha}}V( t ) \le \chi V( t ) - \eta$</tex-math> </inline-formula> . 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.