A numerical procedure to compute stabilizing state feedback gains for linear time-varying periodic systems

A procedure to synthesize stabilizing controllers for linear time-varying periodic continuous-time systems is proposed in this paper. The controller is a periodic state-feedback gain whose construction is based on the utilization of the transition matrix of the open-loop system, and the stability of the closed-loop system is guaranteed if the system is controllable and if a observability-based condition is satisfied. The periodic state feedback gain is obtained through the numerical integration of two differential matrix equations over two periods, being the resolution of such equations considerably simpler and computationally more viable than the resolution of Ricatti differential equations considered in the standard LQR approach. Some examples illustrates the validity of the technique.