@article{oai:nagoya.repo.nii.ac.jp:00010305,
 author = {Hayakawa, Yoshikazu and Jimbo, Tomohiko},
 journal = {47th IEEE Conference on Decision and Control (CDC 2008)},
 month = {Dec},
 note = {This paper considers discrete-time periodic linear systems and their Floquet transformations, by which the periodic systems can be equivalently transformed to time-invariant ones. When the system matrix is nonsingular, it is very easy to derive the discrete-time Floquet transformation, however, when the system matrix is singular,  the derivation is essentially different from the continuous-time case. A necessary and sufficient condition for Floquet transformation to exist has been already known and this paper aims to give a simpler proof, by which all the similarity classes of Floquet transformations could be made clear. And also an extension of Floquet transformations to non-autonomous systems is shown.},
 pages = {5140--5145},
 title = {Floquet Transformations for Discrete-time Systems: Equivalence between periodic systems and time-invariant ones},
 year = {2008}
}