The Duality Relation between Maximal Output Admissible Set and Reachable Set

The concept of positive invariance is central to several problems in control theory, such as constrained control, disturbance rejection and robustness analysis. This paper considers two specific types of positively invariant sets, known as the maximal output admissible set and reachable set, determined for linear continuous-time system. In this paper, the inner and outer approximations of both the maximal output admissible set and reachable set are established by using the forward Euler approximated system and the modified zero order hold system. The main purpose is to show that there exists the duality relation between the maximal output admissible set and reachable set. An application of these two positively invariant sets to characterizing the L^p-induced norm of Hankel operator is discussed.