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On similarity classes of discrete-time Floquet transformations

This paper considers discrete-time Floquet transformations, by which a discrete-time periodic linear system can be transformed to a time-invariant one. The previous researches have made clear when a discrete-time periodic system has its Floquet transformations and also it is known that the system has a lot of Floquet transformations if it has one. This paper defines three new similarities between two Floquet transformations, clarifies some relations among those similarities, and also makes clear how a set of all Floquet transformations can be split into a finite number of equivalence classes.