Discrete Variable Structure Control for Uncertain Linear Multivariable Systems

Abstract

The methodology of variable structure with sliding mode is proven to be very successful in controlling uncertain continuous-time dynamical systems. When the system is sampled or purely discrete, the invariance property of sliding mode, which is originally a continuous-time concept, no longer hold and the reaching condition has to be modified to allow a pseudo-sliding mode. Moreover, the state dependency of parametric uncertainties makes the satisfaction of reaching condition considerably more difficult especially in multivariable systems. These difficulties have offered challenges that attracted a great deal of research interests. This thesis presents theoretical results on the discrete variable structure control of uncertain linear multivariable systems using the concepts of sliding mode and switching sector. It considers both the stale and output feedback cases for systems with addictive uncertainties and the state feedback case for systems with parametric uncertainties. The thesis also presents a sliding surface design procedure for single-input systems based on the version of discrete variable structure control developed by OJ'. Eduardo Misawa.