Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

7SMC of Switched State-Delayed Hybrid Systems: Continuous-Time Case

7.1 Introduction

SMC theory and methodologies have been developed for many kinds of systems such as uncertain systems, time-delay systems, and stochastic systems. Unfortunately, little progress has been made toward solving SMC of switched hybrid systems. The research in this area has not been fully investigated and still remains challenging. In this chapter, we will investigate the SMC design problem for continuous-time switched hybrid systems with time-varying delay. First, the original system is transformed into a regular form through model transformation, and then by designing a linear sliding surface, the dynamical equation for the sliding mode dynamics is derived. By utilizing the average dwell time approach and the piecewise Lyapunov function technique, a delay-dependent sufficient condition for the existence of a desired sliding mode is proposed, and an explicit parametrization of the desired sliding surface is also given. Since the obtained conditions are not all expressed in terms of strict LMIs (some matrix equality constraints exist), the CCL method is exploited to cast them into a sequential minimization problem subject to LMI constraints, which can be easily solved numerically. Then, a discontinuous SMC law is synthesized, by which the system state trajectories can be driven onto the prescribed sliding surface in a finite time and maintained there for all subsequent time. Since the designed SMC ...