A study on the state set invariance for a class of discrete-time linear control systems

Abstract

This paper considers the state set invariance for a class of linear control systems over the discrete time horizon. Given a state set and a control set, the author proposes the methodology to design a state feedback controller and its corresponding maximum invariant subset of the state set. The corresponding invariant subset means that with the controller any state starting from the subset remains in the subset at all times. Fixing the controller, the necessary and sufficient condition for the maximum invariant subset to be the state set itself is first derived. For the systems not satisfying the condition, the author characterizes the corresponding maximum invariant subset based on the spectral analysis of matrices. Numerical examples for different cases are given to illustrate the proposed computation techniques.