On the Use of the Averaging Method for the Characteristic Multiplier Placement Problem

This paper proposes a novel approach for desining a periodic state feedback control law for a class of continuous-time linear periodic systems. The control law generates the sufficiently high frequency sinusoidal in the coefficient of the closed loop systems, then the closed loop solution is shown to be exponentially stable based on the averaging method. It is also shown that the closed loop solution is approximated by the solution of the average system.