Exponential Synchronization for Variable-order Fractional Complex Dynamical Networks via Dynamic Event-triggered Control Strategy

This paper is concerned with the global exponential synchronization issues for variable-order fractional complex dynamic networks (FCDNs). Firstly, a new derivative operator, which is called as the generalized Caputo variable-order fractional derivative, is developed, and some properties and lemmas are rigorous proved. Secondly, a new dynamic event-triggered control mechanism is designed to realize the synchronization objective, where the generalized Caputo variable-order fractional derivative is applied to characterize the evolution state of internal dynamic variable. And the exclusion for Zeno behavior is verified by contradiction analysis method. Thirdly, a class of functions, which is an extension of the Lipschitz function, is introduced to model the nonlinear dynamics for the considered system. With the aid of fractional Lyapunov functional method, some auxiliary functions and advanced mathematical analysis techniques, the global exponential synchronization conditions are established in terms of linear matrix inequalities (LMIs). Finally, the correctness of the theoretical results and the feasibility of the designed controller in this paper are confirmed by applying a numerical simulation example.