On controllability of discrete-time linear ensemble systems with linear parameter variation

Abstract

The control of ensembles of dynamic systems is receiving increased attention due to newly emerging applications in science and engineering. Controllability of linear ensemble systems has been extensively studied in recent years with a special focus on continuous-time systems. In this paper, we study a class of discrete-time linear ensemble systems, whose natural dynamics vary linearly with the system parameter, as well as a class of discrete-time bilinear ensemble systems. We establish explicit controllability and reachability conditions for these ensemble systems and show that stability plays an important role for controllability of the linear ensemble systems. In addition, we analyze how the controllability can be affected through discretization for continuous-time linear ensemble systems and provide a sufficient condition under which controllability property is invariant with discretization.