A Periodic State Feedback Control Law by Raising Frequency for a Class of Linear Periodic Continuous-Time Systems

摘要

This paper proposes an explicit formula for designing a periodic state feedback control law for a class of linear periodic continuous-time systems. The proposed control law sufficiently raises the frequency of a periodic coefficient matrix of a resultant closed-loop system so that the closed-loop system is exponentially stabilized, which is proved by introducing an averaging technique with quantitative evaluation. This enables closed-loop characteristic multipliers to converge to desired place, which are arbitrarily specified by the pole placement design for an averaged linear time-invariant system. The effectiveness of the proposed control law is demonstrated in a numerical example of attitude control of small satellites with magnetic actuator.