Design of Periodic Event-Triggered Sliding Mode Control

Abstract

This chapter presents an event-triggering approach to the design of sliding mode control (SMC) for an uncertain linear dynamical system. In the event-triggering mechanism, only discrete measurements are used to verify the event condition for generating a sequence of triggering instants. Such a triggering mechanism is known as the periodic triggering mechanism. Due to the periodic evaluation, the event condition in the triggering mechanism can only be detected at a time instant, which is a multiple of sampling period, although it may hold before this instant. The design of SMC in the periodic event-triggering framework becomes even more complicated because of the dependency of switching gain on the triggering parameter. This chapter presents a novel method of designing the periodic triggering mechanism-based SMC that can control the plant under external perturbations. In our approach, we decouple the design of event condition and the switching gain of SMC by choosing appropriately the sampling period for the periodic evaluation. Therefore, one may design the switching gain first to obtain a suitable sampling period so that the desired bound for the state trajectories can be achieved by the event-triggered controller. Finally, the simulation results are presented to demonstrate the performance of the proposed triggering mechanism.