Time scale reachability and controllability of time‐varying linear systems

Abstract

In this paper, we investigate the analysis of reachability and controllability for time‐varying linear systems evolving on nonuniform time domains also known as arbitrary time scales. Based on appropriate operators, some necessary and sufficient conditions are derived to guarantee the reachability for this class of systems using linear algebra tools. Furthermore, a link between optimality and the proposed operators is given. Then, the connection between reachability and controllability analysis on arbitrary time scales is discussed. Through the paper, some examples illustrate the theoretical results.

Existence, stability and controllability results for a class of switched evolution system with impulses over arbitrary time domain

“…In Ben Nasser et al. ( 2021 ), the authors studied the reachability and controllability results for the time-varying linear systems evolving on time scales while in Yasmin et al. ( 2020 ), the authors investigated the controllability results for the linear impulsive adjoint dynamic system on time scale.…”