相关论文: Analysis of Linear Time-Varying & Periodic Systems
Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution…
Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex,…
In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are…
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends…
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…
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…
In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…
In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $ U(t,0)\equiv P(t)e^{\frac{-i}{\hbar}H_F t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet…
The article presents a rather surprising Floquet-type representation of time-varying transition matrices associated with a class of nonlinear matrix differential Riccati equations. The main difference with conventional Floquet theory comes…
Stable inverse systems for periodically time-varying plants are essential for feedforward control and iterative learning control of multirate and periodic systems, yet existing approaches either require complex-valued Floquet factors and…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…
This paper introduces a conversion matrix method for linear periodically time-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling that offers precise and computationally efficient results to enable rapid design iteration…
Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the…
This paper studies closed-loop identification of linear periodically time-varying (LPTV) plants, with emphasis on open-loop unstable plants for which open-loop experiments are not practically available. The central contribution is an exact…
The aim of our paper is to formulate and solve problems concerning linear multiple periodic recurrence equations. Among other things, we discuss in detail the cases with periodic and multi-periodic coefficients, highlighting in particular…
Periodically driven systems provide a powerful platform for quantum multiparameter estimation. Constructing a static effective Hamiltonian in a proper rotating frame is commonly employed to assess the attainable precision. However, such an…
Periodically driven (Floquet) phases are attractive due to their ability to host unique physical phenomena with no static counterparts. We propose a general approach in nontrivially devising a square-root version of existing Floquet phases,…