H ∞ $$ {H}_{\infty } $$ Synchronization of Semi-Markovian Switching Complex-Valued Networks With Time-Varying Delay: A Delay-Dependent Event-Triggered Mechanism

Abstract

This paper focuses on the $H_{\infty }$ synchronization issue for delayed semi-Markovian switching complex-valued networks via the delay-dependent event-triggered mechanism. For the first time, in order to reduce the redundant information transmission and the number of false triggers, a novel event-triggered mechanism is proposed, which involves the network-induced time delay and the latest triggered signal. Second, based on the proposed delay-dependent event-triggered control scheme, the desired results can be realized. Specifically, by utilizing the stochastic analysis technique and Lyapunov stability theory as well as mixed reciprocally convex inequalities, some sufficient less conservative criteria are achieved to ensure the synchronization error system realize the globally asymptotically mean-square stability with a pre-established $H_{\infty }$ disturbance performance. Furthermore, the expected controller gain matrices can be explicitly designed by solving some solvable matrix inequalities. At the end of paper, an illustrative example with simulations is presented to demonstrate the feasibility and effectiveness of the proposed delay-dependent event-triggered scheme.