Finite-time stabilization of linear systems by bounded event-triggered and self-triggered control

Abstract

This paper is concerned with finite-time stabilization (FTS) of linear systems by bounded event-triggered control (ETC) and self-triggered control (STC). A bounded linear ETC is firstly designed, where the time-varying control gain is only scheduled on a specified time determined by an event-triggered mechanism, such that the FTS of the closed-loop system is achieved and the communication resources are saved. Moreover, the corresponding STC, in which the updates of control law are determined by a self-triggered mechanism that only needs to monitor the previous triggered states, is designed. Specially, by exploring the properties of the parametric Lyapunov equation, the designable minimal inter-event time of the established ETC and STC is obtained, such that the Zeno phenomenon is avoided. In addition, the finite-time semi-global stabilization and the fixed-time (prescribed finite-time) stabilization of linear systems are achieved by bounded ETC and STC. What needs to be emphasized is that the finite-time stabilization in this paper can be called as the practical finite-time stabilization since the state converges to zero exponentially with a fast convergence rate after a designable time. Finally, the established algorithms are used to the design of the spacecraft rendezvous control system and their effectiveness is verified by simulations.