Convergence-Rate-Based Event-Triggered Mechanisms for Quasi-Synchronization of Delayed Nonlinear Systems on Time Scales

Most of the existing event-triggered mechanisms (ETMs) were designed according to the difference between the quadratic form of measurement errors and the quadratic form of sampling states (or real-time states). In order to reduce the amount of data transmission and develop ETMs for continuous-time and discrete-time delayed nonlinear systems (NSs) simultaneously, this article investigates quasi-synchronization (QS) of NSs on time scales based on a novel ETM, which is designed according to the convergence rate instead of measurement errors of the addressed systems. First, a novel ETM is designed under known nonlinear dynamics, and it is demonstrated that QS with given convergence rate and error level can be achieved under matrix inequality criteria. Second, if the nonlinear functions are unknown, we adapt our ETM to handle this special case. Not only QS but also complete synchronization with given convergence rate can be achieved under the ETMs. If the constructed Lyapunov functions passes through 0, the designed ETM will keep it at the origin. In this case, finite-time synchronization is achieved. Third, under the designed ETMs, it is proved that Zeno behavior can be excluded. At last, four numerical simulations are presented to demonstrate the feasibility and the advantage of the designed ETMs in this article.