Sliding Mode Control of Uncertain Stochastic Hybrid Delay Systems with Average Dwell Time

This paper investigates the problem of sliding mode control (SMC) for uncertain switched stochastic system with time-varying delay. The system under consideration is concerned with the stochastic dynamics and deterministic switching laws. An integral sliding surface is constructed and the stable sliding mode is derived. A sufficient condition for mean-square exponential stability of the sliding mode is developed under a class of switching laws based on the average dwell time method. Variable structure controllers are designed to guarantee the existence of the sliding mode from the initial time. An illustrative example is used to demonstrate the effectiveness of the proposed scheme.