Event-Triggered Synchronization in Networks of Variable-Order Fractional Piecewise-Smooth Systems With Short Memory

This article investigates the exponential synchronization issue for networks of variable-order fractional piecewise-smooth systems with short memory, where each node is modeled to satisfy $\sigma $ -QUAD condition, and possess the incommensurate order. First, the generalized Caputo variable-order fractional derivative (VOFD) operator is defined, and some properties and lemmas with respect to VOFD are developed. Second, the dynamic event-triggered control mechanism is designed, where the additional internal dynamic variable is subject to the nonlinear variable-order fractional dynamical system with incommensurate order. Third, by exploiting the Lyapunov stability theory and some auxiliary inequality techniques, the exponential synchronization criteria are established in terms of linear matrix inequalities (LMIs) under the designed control scheme. In addition, the nonexistence of Zeno behavior is proved by contradiction. Finally, a numerical example is given to illustrate the effectiveness of the main results.