To the robust stabilization problem of linear periodic systems

In this paper we extend the classical state-feedback pole assignment problem of time-invariant systems to linear periodic systems. This concept is used to present conditions for the robust stabilizability of systems, in the sense that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. Upper bounds on the norm of the feedback matrix and on the transient response are also minimized, and an estimation is given of the maximum disturbance which can be made to the closed-loop system such that stability is retained.