Sliding Mode Control for Linear Time-Delay System

Abstract

This paper is concerned with sliding mode control for a linear system with time delay in the state. We consider here a design method of a hyperplane as a switching surface and a simple control which brings the trajectory on the surface. And, by using the zero dynamics technique, it is shown that the sliding mode system on the surface is stable. The stabilizability condition is given by a matrix inequality which becomes an LMI (linear matrix inequality) in a special case.