Stabilizability and detectability of linear periodic systems

In this paper, four characterizations of stabilizability and detectability of linear periodic systems are considered. Two of them look as natural extensions of the classical definitions given for time-invariant systems. The remaining two are modal characterizations which turn out to be useful in the analysis of the periodic Lyapunov and Riccati equations. It is shown that all these notions of stabilizability (and detectability) are in fact equivalent to each other.One of the various definitions calls for the existence of the Kalman canonical decomposition of periodic systems. This issue is addressed in the Appendix.