Continuous-Time Linear Periodic Systems: A Note on the Controllability Interval Length

Abstract

Continuous-time linear systems with periodic coefficients of period T are considered in this paper. We study the question of the controllability interval length of periodic systems. It is known that a controllable T-periodic system is controllable over intervals of the length kT where k is the degree of the minimal polynomial of the monodromy matrix. It is proved that this boundary kT is exact and cannot be decreased. It is proved that controllability of a T-periodic system on some interval of the length sT depends on the initial moment, in general.