ε-Dependent/Independent Dynamic Event-Triggered Control of Switched Two-Time-Scale Systems

This article investigates the event-triggered composite control problem for switched two-time-scale systems (TTSSs). First, the stabilization problem of switched TTSSs under switching composite control is addressed. Unlike existing results that require the singular perturbation parameter (SPP) to be sufficiently small or to satisfy specific linear matrix inequality conditions, an explicit upper bound of the SPP is derived. Then, both SPP-dependent and SPP-independent dynamic event-triggered mechanisms are developed to reduce the computational burden associated with control signal updates in switched TTSSs. These mechanisms are novel in that they incorporate the boundary layer system and explicitly balance the fast and slow time-scale dynamics. Furthermore, two sufficient stability conditions are established: one concerning the upper bound of the SPP and the other concerning the mode-dependent average dwell time, ensuring the stability of switched TTSSs under the respective mechanisms. In addition, Zeno's behavior is excluded in both cases. Finally, three numerical examples, including a comparative study, are provided to demonstrate the effectiveness and advantages of the proposed results.