Abstract
This paper considers the stabilization of the linear periodic discrete-time system by the use of a linear periodic state-variable feedback. Let the transition matrix of the closed-loop system be Y(t, s). Then the stability of the closed-loop system depends on the eigenvalues of Y(τ, 0), where τ is the period. It is shown that there exists a periodic state-variable feedback gain matrix such that the eigenvalues of Y(τ, 0) take pre-assigned values if and only if an open-loop system is completely reachable.
