Dynamic Event-Triggered Sliding Mode Control: Dealing With Slow Sampling Singularly Perturbed Systems

This brief endeavors to investigate the sliding mode control (SMC) issue of the networked singularly perturbed systems (SPSs) under slow sampling. For the energy saving purpose in network communication, a dynamic event-triggered mechanism is introduced to SMC design. By considering the structure characteristics of the controlled system, a novel sliding function is constructed with taking the singular perturbed matrix $E_\varepsilon $ into account properly. With the aid of some appropriate Lyapunov functionals, the sufficient conditions are derived to ensure the asymptotic stability of the sliding mode dynamics and the reachability of the specified sliding surface. Besides, it is shown that the quasi-sliding motion is dependent on the dynamic event-triggered parameters and its bound converges to a constant. The solving algorithm for the dynamic event-triggered SMC law is formulated in a convex optimization framework. Finally, an numerical example is provided to illustrate the effectiveness of the proposed results.