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When is a periodic discrete-time system equivalent to a time-invariant one? (English) Zbl 1035.93505
Summary: We give the precise conditions under which a periodic discrete-time linear state-space system can be transformed into a time-invariant one by a change of the basis. Thus our theory is the discrete-time counterpart of the classical theory of Floquet transforms developed by Floquet and Lyapunov in the 1800s for continuous-time systems. We state and prove a necessary and sufficient condition for a discrete-time Floquet transform to exist, and we give a construction for the transform when it does exist. Our results also extend to generalized state-space, or descriptor, systems.

MSC:
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
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