Classification and characteristics of Floquet factorisations in linear continuous-time periodic systems. (English) Zbl 1158.34328
Summary: This article has two purposes. Firstly, the article is devoted to collecting basic facts about the Floquet theorem and various Floquet factorisation algorithms claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems. Secondly, the article presents a unified representation framework for various Floquet factorisations 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 factorisations; (ii) characteristics of Floquet factors; (iii) relationships and properties among Floquet factorisations. Most results are reported for the first time, while the others are generalised versions of existing ones.
MSC:
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 34A30 | Linear ordinary differential equations and systems |
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