Input-to-state practical stability of switched affine systems with time-varying delay: an event-triggered mechanism

Abstract

This paper investigates the problem of the input-to-state practical stability for switched affine systems with time-varying delay and essentially bounded exogenous disturbance. The presence of affine terms makes switched systems have multiple switched equilibria and brings further difficulties in the stability analysis, control synthesis and avoiding Zeno behaviours compared with the non-affine switched systems. To overcome these difficulties, first, a convex combination approach is employed to acquire a set of attainable equilibria limited by the system matrix, the delay term matrix, and affine terms. Second, a mode-dependent event-triggered mechanism with sampled-data information is established, which not only ignores Zeno behaviour but also effectively reduces network resource waste. An input-to-state practical stability criterion is proposed for the closed-loop system by converting the event-triggered control system into a time-delay system and introducing a less conservative time-dependent Lyapunov–Krasovskii functional. Moreover, a sampled-data switching law and a set of executable controllers are also co-designed. Finally, an application example of the flyback DC–DC converter demonstrates the efficiency of the proposed result.