Local stabilization of linear distributed parameter systems under constraints on both control and its rate via compensator

This note addresses the stabilization problem for linear infinite-dimensional systems, partially observed, in the presence of inequality constraints on both control and its rate. We propose a stabilizing state feedback on the estimated state, reconstructed from a full state observer. So, we give the necessary and sufficient conditions under which the constraints are satisfied, by an adequate use of the positive invariance concept. The approach presented allows to determine a suitable stability domain - in which the constraints are respected - for the closed loop system.