A Gramian-based controller for linear periodic systems

This note proposes a new design method for the control of linear time-periodic systems. The method is based on the reachability Gramian and a specific form for the feedback gain matrix to build a novel control law for the closed-loop system. The new controller allows assignment of all the invariants of the system. Calculating the feedback requires solving a matrix integral equation for the periodic Floquet factor of the state-transition matrix of the closed-loop system.