An event-triggered mechanism to observer-based sliding mode control of fractional-order uncertain switched systems

This chapter deals with the problem of observer-based event-triggered sliding mode control for fractional-order uncertain switched systems with a positive order less than one. First, a fractional-order state observer is designed, based on which a fractional-order integral sliding surface function is proposed. Then, utilizing the estimated observer and sliding mode error vectors, an event-triggered condition is constructed to decide whether the current control signal should be updated or not. Besides, sufficient conditions are derived in the form of linear matrix inequalities (LMIs) to ensure finite-time stability of the augmented closed-loop system by adopting an average dwell time approach. Thereafter, to avoid the occurrence of infinitely many triggers within a finite time, this chapter also discusses the Zeno behavior and refines the results in the previous literature. Finally, to illustrate the effectiveness and superiority of the proposed method, three numerical simulations are provided.