Classification and Characteristics of Floquet Factorizations in Linear Continuous-Time Periodic Systems
نویسنده
چکیده
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.
منابع مشابه
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 characteristic...
متن کاملReal Floquet factors of linear time-periodic systems
Floquet theory plays a ubiquitous role in the analysis and control of time-periodic systems. Its main result is that any fundamental matrix X(t, 0) of a linear system with T -periodic coefficients will have a (generally complex) Floquet factorization with one of the two factors being T -periodic. It is also well known that it is always possible to obtain a real Floquet factorization for the fun...
متن کاملA Unified Floquet Theory for Discrete, Continuous, and Hybrid Periodic Linear Systems
In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We develop a comprehensive Floquet theory including Lyapunov transformations and their various stability preserving properties, a unified Floquet theorem which es...
متن کاملFactorizing the Monodromy Matrix of Linear Periodic Systems
This note proposes a new approach to computing the Kalman canonical decomposition of finite-dimensional linear periodic continuous-time systems by extending the Floquet theory. Controllable and observable subspaces are characterized by factorizing the monodromy matrix. Then, the conditions for the existence of several periodic Kalman canonical decompositions are extensively studied. The relatio...
متن کاملA Software for Prediction of Periodic Response of Non-linear Multi Degree of Freedom Rotors Based on Harmonic Balances
It is the purpose of this paper to introduce a computer software that is developed for the analysis of general multi degree of freedom rotor bearing systems with non-linear support elements. A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotor dynamic systems is addressed which is based on the harmonic balance technique. By utilizing ...
متن کامل