Sliding mode control of switched hybrid systems with time-varying delay

This paper is concerned with the sliding mode control of a continuous-time switched system with time-varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced-order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory.