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In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…

Analysis of PDEs · Mathematics 2018-08-17 Swann Marx , Yacine Chitour , Christophe Prieur

In this paper, We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and comparison principle for Lyapunov - like functions, we give some sufficient criterias for the…

Dynamical Systems · Mathematics 2007-05-23 Le Van Hien

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…

Dynamical Systems · Mathematics 2014-05-29 Samuel Bernard , Fabien Crauste

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

In this paper we consider the global stability of solutions of an affine 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

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…

Analysis of PDEs · Mathematics 2015-03-13 Tomas Caraballo , Mohamed Ali Hammami , Lasaad Mchiri

Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases,…

Analysis of PDEs · Mathematics 2020-11-03 Oana Brandibur , Eva Kaslik

Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…

Analysis of PDEs · Mathematics 2015-09-22 Rasha Al Jamal , Amenda Chow , Kirsten Morris

This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…

Systems and Control · Computer Science 2017-11-27 Atreyee Kundu , Debasish Chatterjee

In this paper, a fractional derivative with short-term memory properties is defined, which can be viewed as an extension of Caputo fractional derivative. Then, some properties of the short memory fractional derivative are discussed. Also, a…

Dynamical Systems · Mathematics 2020-07-14 Xudong Hai , Guojian Ren , Yongguang Yu , Lipo Mo , Conghui Xu

In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…

Dynamical Systems · Mathematics 2019-02-13 H. Zhu , Z. Li , X. He

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

Dynamical Systems · Mathematics 2008-03-27 M. De la Sen

We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…

Optimization and Control · Mathematics 2020-03-09 Hanaa Zitane , Ali Boutoulout , Delfim F. M. Torres

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance:…

Dynamical Systems · Mathematics 2019-11-27 Florian Monteghetti , Ghislain Haine , Denis Matignon

In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the…

Classical Analysis and ODEs · Mathematics 2025-09-05 Vu Trong Luong , Nguyen Duc Huy , Nguyen Van Minh , Nguyen Ngoc Vien

In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…

Dynamical Systems · Mathematics 2025-04-03 Jinyuan Pan , Guiling Chen

In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…

Optimization and Control · Mathematics 2026-03-25 Kunal Garg

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

This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…

Numerical Analysis · Mathematics 2024-07-15 Kai Diethelm , Safoura Hashemishahraki , Ha Duc Thai , Hoang The Tuan

Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis