Stabilizability and a separation principle for periodic orbits

In this paper, we derive a result for stabilizability and a separation principle for periodic orbits. First, using degree theory, we derive a necessary condition for local asymptotic stabilizability of periodic orbits. This condition is similar to the famous Brockett's necessary condition (1983) for local asymptotic stabilizability for equilibria. Next, we derive a separation principle for periodic orbits. Our separation principle states that if a state feedback system defined in the neighborhood of a periodic orbit is asymptotically stabilizable and if an exponentially good state estimator is known, then the composite state feedback-state estimator scheme is locally orbitally asymptotically stable.