Adaptive Variable Structure Control of Linear Delayed Systems

Abstract

This brief deals with the stabilization of a class of time-delay systems subject to external disturbance vectors whose bounds are not known. A continuous adaptive variable structure controller is synthesized to guarantee that the motions of the sliding surface are uniformly exponentially convergent to a ball with any prespecified exponential convergence rate towards it. Furthermore, the reduced-order sliding mode dynamics as well as the deviation from ideal sliding motion are uniformly exponentially convergent to a ball whose radius is minimized and the exponential convergence towards it is maximized. The problem is formulated as an optimization problem with LMI constraints. Finally, an example is included to illustrate the results developed in this brief.