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A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…

Dynamical Systems · Mathematics 2013-04-11 Pete Donnell , Murad Banaji

We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…

Adaptation and Self-Organizing Systems · Physics 2025-12-03 Tiago Pereira

We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes…

Probability · Mathematics 2012-10-02 Antonius B. Dieker , Jinwoo Shin

This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…

Dynamical Systems · Mathematics 2016-03-18 Hua Shao , Yuming Shi , Hao Zhu

This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…

Dynamical Systems · Mathematics 2022-09-15 Alejandro Castaño , Carlos Cuvas , Alexey Egorov , Sabine Mondié

We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is…

Dynamical Systems · Mathematics 2024-10-07 Laurent Baratchart , Sébastien Fueyo , Gilles Lebeau , Jean-Baptiste Pomet

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

Systems and Control · Electrical Eng. & Systems 2022-08-12 Francesco Ferrante , Giorgio Valmorbida

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…

Dynamical Systems · Mathematics 2023-08-11 Vitalii Slynko , Sergey Dashkovskiy , Ivan Atamas

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the…

Optimization and Control · Mathematics 2022-05-17 Iasson Karafyllis , Pierdomenico Pepe , Yuan Wang , Antoine Chaillet

In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary…

Optimization and Control · Mathematics 2023-05-17 Jake Welde , Matthew D. Kvalheim , Vijay Kumar

We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expectations with a boundedly rational, and genuinely sticky,…

Dynamical Systems · Mathematics 2017-11-22 Pavel Krejci , Harbir Lamba , Dmitrii Rachinskii

In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…

Dynamical Systems · Mathematics 2023-06-26 Jacopo Piccini , Elias August , Sigurdur Hafstein , Stefania Andersen

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

Probability · Mathematics 2013-10-10 John A. D. Appleby , Jian Cheng , Alexandra Rodkina

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…

Systems and Control · Electrical Eng. & Systems 2023-02-13 Adrien Banse , Zheming Wang , Raphaël M. Jungers

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

Optimization and Control · Mathematics 2010-09-08 Debasish Chatterjee , Daniel Liberzon

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

We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…

Probability · Mathematics 2007-05-23 Ramon van Handel

We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of…

Optimization and Control · Mathematics 2012-10-29 Philippe Jouan , Naciri Saïd

In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…

Dynamical Systems · Mathematics 2022-07-06 Robert Vrabel

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…

Systems and Control · Computer Science 2015-09-07 Kwang-Ki K. Kim , Richard D. Braatz