Discrete-time linear periodic systems: A note on the reachability and controllability interval length (Q1085117)

Discrete-time linear systems with periodic coefficients of period T are considered in this paper. The reachability and controllability indices at time t for periodic systems, \(\mu_{rt}\) and \(\mu_{ct}\) are defined. It is shown that the reachability [controllability] subspace at time t does coincide with the reachability [controllability] subspace over the interval \((t-\mu_{rt},T,t)\) \([t,t+\mu_{ct}T)]\) and properly includes the reachability [controllability] subspace over the interval \((t- (\mu_{rt}-1)T,t)\) \([(t,t+(\mu_{ct}-1)T)]\).