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Floquet Factorizations in Linear Continuous-Time Periodic Systems Qiu Peng, Hohai University Abstract This paper discusses the algorithms of Floquet factorizations for the state transition matrices claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems，and compares the two methods of standard Floquet factorizations: Cauchy Integration Formula and Jordan Canonical Forms. The main contents are: Floquet factorizations by Jordan/Cauchy algorithms and the basic mathematical concepts involved in; the relationships in between the two methods of standard Floquet factorizations. Key Words: Matrix Logarithm, Floquet factorizations, algorithm \ 1.Introduction The Floquet theorem, or more generally Floquet theory, can be traced back to 1883, which presents us Floquet factorizations for state transition matrices, fundamental matrices and solutions to periodic differential equations. Perodic differential equations frequently appear in control and system applications related to finite-dimensional linear continuous-time periodic (FDLCP) modelings. Typical problems include stabilization of helicopter rotors and ships in waves, and reduction of electro-mechanical oscillations or swing in electricity generators. As a matter of fact, the Floquet theorem is originally developed to transfer periodic differential equations into ones with constant coefficients and has been one of the kernel results for analysis and synthesis in FDLCP control systems, without which some important developments in the FDLCP field may not be attainable. For example, asymptotic stability in FDLCP systems can be better dealt with if Floquet factorizations are available; control can be implemented via real Floquet factorizations; harmonic controllability criteria are established also with Floquet factorizations; last but not least, frequency-domain aspects about FDLCP systems can be examined by means of Floquet factorizations. It is worth mentioning that Floquet theory has been exte