Stabilization of Input Delay Systems by Using Sliding Mode Control

Abstract

In this paper, we consider the stabilization problem of linear systems with time-delay at the input by using a sliding mode control. Sliding Mode Control (SMC) is a well-known robust control method for systems with model uncertainties and disturbances and a large number of the design methods for finite dimensional systems have been proposed. However there are a few design methods which are applicable for input-delay systems. To overcome the drawback, we analyze the stability of input-delay systems with switching inputs by transforming the systems into the equivalent systems with time-varying feedback gain. As a result, we show that input-delay systems cannot be asymptotically stabilized by the SMC with signal function. Then we derive a sufficient condition for asymptotic stability of the systems with SMC. Thereafter we propose a SMC design method for systems with uncertain delay at the input. The effectiveness of the proposed methods are illustrated by numerical simulations.