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We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an…

Quantum Physics · Physics 2017-11-22 Meenu Kumari , Eduardo Martin-Martinez , Achim Kempf , Shohini Ghose

Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…

Mathematical Physics · Physics 2024-12-12 Hong Qin

In this brief note, we establish a novel criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the presence of possibly unbounded perturbations (external disturbances). To prove the result,…

Dynamical Systems · Mathematics 2021-01-05 Robert Vrabel

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…

Systems and Control · Electrical Eng. & Systems 2019-11-04 Yohei Hosoe , Tomomichi Hagiwara

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…

Dynamical Systems · Mathematics 2017-05-31 Nina Xue , Xiong Li

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

This note is concerned with the stability and stabilization of the linearized spacecraft attitude control system. Necessary and sufficient conditions are respectively provided to guarantee that the considered systems are polynomially stable…

Dynamical Systems · Mathematics 2015-04-02 Bin Zhou

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…

Pattern Formation and Solitons · Physics 2009-11-13 Y. Sivan , G. Fibich , B. Ilan , M. I. Weinstein

This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…

Dynamical Systems · Mathematics 2011-04-08 Ivo Petras

We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…

Dynamical Systems · Mathematics 2021-04-06 M. M. Shumafov , V. B. Tlyachev

Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…

Optimization and Control · Mathematics 2017-03-14 Corentin Briat , Mustafa Khammash

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

Dynamical Systems · Mathematics 2013-06-12 A. Gorban , I. Tyukin , E. Steur , H. Nijmeijer

This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new geometric characterization of the…

Systems and Control · Computer Science 2013-04-11 Ian R. Petersen

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…

Optimization and Control · Mathematics 2020-08-05 Muhammad F. Emzir , Matthew J. Woolley , Ian R. Petersen

In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis , Pierdomenico Pepe , Zhong-Ping Jiang

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized…

Analysis of PDEs · Mathematics 2010-12-22 Blake Barker , Mathew A. Johnson , Pascal Noble , L. Miguel Rodrigues , Kevin Zumbrun

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under…

Optimization and Control · Mathematics 2018-09-17 Nadhem Echi , Boulbaba Ghanmi

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…

Analysis of PDEs · Mathematics 2021-07-28 Zhiwu Lin

The question for linear stability of spatially periodic waves for the Boussinesq equation (the cases $p=2,3$) and the Klein-Gordon-Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their…

Analysis of PDEs · Mathematics 2012-02-13 Sevdzhan Hakkaev , Milena Stanislavova , Atanas Stefanov

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…

Optimization and Control · Mathematics 2019-09-18 Saman Cyrus , Laurent Lessard