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A delayed feedback control framework for stabilizing unstable periodic orbitsof linear periodic time-varying systems is proposed. In this framework,act-and-wait approach is utilized for switching a delayed feedback controlleron and off alternately at every integer multiples of the period of the system.By analyzing the monodromy matrix of the closed-loop system, we obtainconditions under which the closed-loop system's state converges towards aperiodic solution under our proposed control law. We discuss the application ofour results in stabilization of unstable periodic orbits of nonlinear systemsand present numerical examples to illustrate the efficacy of our approach.

Stabilizing Unstable Periodic Orbits with Delayed Feedback Control in Act-and-Wait Fashion