Asymptotic stabilization of a class of continuous-time linear periodic systems

In this paper, the problem of the asymptotic stabilization of a class of continuous-time linear periodic systems is considered. First, under a simplifying assumption, necessary conditions, involving the concept of left eigenvector, are derived for the asymptotic stabilization of continuous-time linear periodic systems belonging to such a class. Then, under the same simplifying assumption, conditions are given under which a static state feedback control law can be designed, in an iterative manner, so that the closed-loop system is π-stable.