Abstract
The concept of positive invariance is involved in several problems in control theory, such as constrained control, disturbance rejection and robustness analysis. This paper considers the two types of positively invariant set, so called maximal output admissible set and reachable set, determined for linear continuous-time systems. There are two main contributions provided: the first result is to clarify the duality relations between maximal output admissible sets and reachable sets. The second issue is to show that the aforementioned positively invariant sets for linear continuous-time system are included in those for the corresponding Euler approximated discrete-time systems and those for the modified sampled models. The inclusions hold monotonically in the case of discrete-time systems, discretized by different sampling periods. Furthermore, the volume of approximated positively invariant set is recovered at any accuracy as sampling period is decreased.
