Event-Triggered Robust Control of Two-Time-Scale Systems Based on Differential Game

This article studies the event-triggered robust control for linear two-time-scale systems (TTSSs) with external disturbance. To reduce control costs and optimize system performance, the stability problem is modeled as a two-player zero-sum differential game between the control policy and the external disturbance. Fast and slow subgames are derived by decoupling the TTSS and the composite optimal control strategy and the worst disturbance are obtained consequently. Furthermore, event-triggered control implementation mechanism is proposed with theoretical analysis using the Lyapunov stability theory, which can deal with the worst disturbance under the equilibrium of continuous control and realize the asymptotic stabilization of the system. Moreover, Zeno behavior of both the fast and slow subsystems is excluded. Simulation examples and a comparison study are conducted to illustrate the effectiveness of the proposed theoretical results.