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This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

Dynamical Systems · Mathematics 2022-06-16 Mark A. Pinsky

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

Analysis of PDEs · Mathematics 2018-08-15 Yue-Hong Feng , Xin Li , Shu Wang

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

It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic…

Dynamical Systems · Mathematics 2024-03-20 Lucas Backes , Davor Dragicevic , Mihaly Pituk

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…

Optimization and Control · Mathematics 2007-05-23 Eugenii Shustin , Emilia Fridman

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…

Dynamical Systems · Mathematics 2017-10-16 Berk Altın , Kira Barton

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

Systems and Control · Electrical Eng. & Systems 2019-11-06 Alin Albu-Schaeffer , Dominic Lakatos , Stefano Stramigioli

We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…

Analysis of PDEs · Mathematics 2025-08-07 L. Miguel Rodrigues , Aric Wheeler

We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both…

Classical Analysis and ODEs · Mathematics 2023-03-20 Douglas R. Anderson , Masakazu Onitsuka

We establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there…

Classical Analysis and ODEs · Mathematics 2012-12-19 Douglas R. Anderson

We introduce a new concept of Hyers-Ulam stability, in which in the size of a pseudosolution of a given ordinary differential equation and its deviation from an exact solution are measured with respect to different norms. These norms are…

Classical Analysis and ODEs · Mathematics 2025-02-24 Davor Dragicevic , Masakazu Onitsuka

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

We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes…

Classical Analysis and ODEs · Mathematics 2018-07-12 Douglas R. Anderson

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…

Dynamical Systems · Mathematics 2018-08-14 Rafael Obaya , Ana M. Sanz

Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…

Analysis of PDEs · Mathematics 2016-04-26 Björn Augner , Birgit Jacob

Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…

Dynamical Systems · Mathematics 2021-03-02 Oana Brandibur , Eva Kaslik

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…

Dynamical Systems · Mathematics 2007-05-23 Ping Wei , Qiang Guan , Wensheng Yu , Long Wang

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…

Quantum Physics · Physics 2016-11-17 Ian R. Petersen

We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…

Functional Analysis · Mathematics 2010-10-05 Marc Burger , Narutaka Ozawa , Andreas Thom

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