Exponential stabilization of linear delayed systems using sliding-mode controllers

This brief deals with the problem of robust exponential stabilization of a class of time-delay systems using sliding-mode controllers. Continuous controllers are synthesized to guarantee that the motions of the sliding surface are uniformly exponentially convergent to a ball whose radius and the rate of exponential convergence toward it can be chosen arbitrarily. 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 toward it is maximized. The problem is formulated as an optimization problem with linear matrix inequality constraints. Finally, an example is included to illustrate the results developed in this brief.