Event-Triggered Fixed-Time Stabilization of Two Time Scales Linear Systems

This article investigates the fixed-time stabilization of uncertain linear time-invariant systems exhibiting two time scales using a state-feedback event-triggered controller. We proceed by emulation and assume that we know a controller that solves the problem in the absence of sampling. We then take sampling into account and present an event-triggered strategy, which consists of two independent sampling mechanisms, associated with the slow and the fast subsystems, respectively. In this setting, the fixed-time stability property becomes practical, where the adjustable parameters are constants used to define the triggering rules. The existence of a strictly positive time between any two successive transmissions is ensured for each transmission law. A numerical example is provided to illustrate the effectiveness of the results.