Robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances

This brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time-varying delays, external disturbances and control saturation. A linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate. The problem is formulated as a two-step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions.