Discrete-time linear periodic systems: gramian and modal criteria for reachability and controllability†

Abstract

Abstract This paper deals with the reachability and controllability of periodic discrete-time systems. First, we supply two necessary and sufficient complete reachability conditions, which apply to reversible and non-reversible systems, respectively. Then, a necessary and sufficient complete controllability condition is provided. This condition, as well as the complete reachability criteria, is given in terms of the reachability gramian matrix. Equivalent modal criteria for reachability and controllability are established in the second part of the paper. Notes † Research Supported by the Centro di Teoria dei Sistemi of the C.N.R. (Milano-Italy) and by M.P.I.