Reachability and Controllability Characterizations for Linear Switched Systems in Discrete Time: A Geometric Approach

This article presents the reachability and controllability characterizations for discrete-time linear switched systems under a fixed and known switching signal. A geometric approach is used, and we are able to provide alternative conditions which are more computationally friendly compared to existing results by utilizing the solution formula at switching times. Furthermore, the proposed conditions make it easier to study the dependency of the reachability and controllability on the switching times and the mode sequences; this is a new result currently not investigated in the literature. Some academic examples are provided to illustrate the novel features found in this study.