On the Approximation of Maximal Output Admissible Set and Reachable Set via Forward Euler Discretization

Abstract

The concept of positive invariance is involved with 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 system. In this paper, the inner approximation of maximal output admissible set and the outer approximation of reachable set are established. The main purpose is to show that there exists the inclusion between the aforementioned positively invariant sets of linear continuous-time system and its forward Euler approximated discrete-time system. The inclusion also holds monotonically in the case of forward Euler approximated systems, discretized by different sampling periods. Finally, the volume of each approximated positively invariant set is recovered at any accuracy when sampling period is decreased.