Feedback Stabilization of Infinite-Dimensional Linear Systems with Constraints on Control and its Rate

The feedback stabilization problem in the presence of nonsymmetrical constraints on both control and its rate is addressed for a class of distributed parameter systems.Necessary and sufficient conditions are established, under which the constraints are satisfied for autonomous infinitedimensional systems. The approach is developed using the semigroup formulation and the positive invariance concept. The main result allows us to determine some suitable positively invariant sets of admissible initial states,in which the constraints are satisfied, with respect to the asymptotically stable closed-loop system.