Classification and characteristics of Floquet factorisations in linear continuous-time periodic systems

This paper has two purposes. Firstly, the paper is devoted to collecting basic facts about the Floquet theorem and various Floquet factorization algorithms claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems. Secondly, the paper presents a unified representation framework for various Floquet factorizations in FDLCP systems, while structural and analytic characteristics about them are examined as well. More precisely, the following aspects are considered: (i) algorithms for Floquet factorizations; (ii) characteristics of Floquet factors; (iii) relationships and properties among Floquet factorizations. Most results are reported for the first time, while the others are generalized versions of existing ones.