Valeriu Prepeliță†, Tiberiu Vasilache‡
Abstract: The controllability of a class of 2D linear time varying continuous time control systems is studied. The state space representation is provided and the formulas of the states and the input-output map of these systems are derived. The fundamental concepts of controllability
and reachability are analysed and suitable controllability and reachability Gramians are constructed to characterize the controllable and the reachable time varying systems. In the case of time invariant 2D systems, some algorithms are developed to calculate different controllability Gramians as solutions of adequate Lyapunov type equations. Corresponding Matlab programs are implemented to solve these Lyapunov equations.
MSC: 93B05, 93C35, 93C05, 93B25
keywords: controllability, Gramians, 2D systems, linear continuous time systems, Lyapunov type equations.
DOI 10.56082/annalsarscimath.2020.1-2.364
†valeriu.prepelita@upb.ro University Politehnica of Bucharest, Department of Mathematics-Informatics, Splaiul Independentei 313, ROMANIA;
‡tiberiu.vasilache@upb.ro University Politehnica of Bucharest, Department of Mathematics-Informatics, Splaiul Independentei 313, ROMANIA
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
