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Factorizing the Monodromy Matrix of Linear Periodic Systems

Abstract This note proposes a new approach to computing the Kalman canonical decomposition of finite-dimensional linear periodic continuous-time systems by extending the Floquet theory. Controllable and observable subspaces are characterized by factorizing the monodromy matrix. Then, the conditions for the existence of several periodic Kalman canonical decompositions are extensively studied. The relations to the Floquet factorization, the Floquet-like factorization, and the period-specific realization are also discussed.