Dynamics Analysis of a Discrete-Time Sliding Mode Controller for Disturbed Linear Systems

Abstract

This paper proposes a discrete-time sliding mode controller for a class of disturbed linear systems and investigates its dynamic characteristics. First, a novel discrete-time sliding mode reaching law is developed by redefining the variation rate of disturbances through a difference function. A disturbance estimation mechanism is then incorporated into the reaching law to compensate for unknown disturbances, and a corresponding discrete-time sliding mode controller is constructed. Second, the main dynamic properties of the closed-loop system are theoretically analyzed, including the width of the quasi-sliding mode domain (QSMD), the finite number of steps required to reach the QSMD, and the bounded convergence of the state variables. It is shown that the switching function can enter the QSMD within a finite number of steps and remain inside it thereafter, while the system states ultimately converge to a bounded neighborhood of the origin. Finally, numerical simulations are carried out to validate the theoretical results and demonstrate the effectiveness of the proposed method. Simulation results demonstrate that the proposed controller can ensure that the switching function reaches QSMD within a finite number of sampling steps and continue to move within QSMD, and the system state will eventually converge.