Asymptotic Assignment of Characteristic Multipliers Using Feedback Control by Raising Frequency

Abstract

The authors introduced in the previous paper a stabilizing feedback control law for a class of linear periodic systems, called feedback control by raising frequency, which exploits the conventional averaging method for stability analysis. In the present paper, the averaging method is rearranged with some new insight in the first place. It includes quantitative evaluation in approximation of solutions even for unstable linear periodic systems. This leads to the proof that feedback control by raising frequency assigns asymptotically characteristic multipliers arbitrarily prescribed, with a quantitative bound of approximation.