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Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

Optimization and Control · Mathematics 2013-12-30 S. Damak , M. Di Loreto , W. Lombardi , V Andrieu

We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…

General Relativity and Quantum Cosmology · Physics 2024-12-16 Gerhard Rein

We show that any solution of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.

Mathematical Physics · Physics 2007-05-23 G. Sardanashvily

We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…

Classical Analysis and ODEs · Mathematics 2012-11-07 Eugene Polulyakh , Vladimir Sharko , Igor Vlasenko

In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…

Systems and Control · Computer Science 2019-03-20 Tinashe Chingozha , Otis T. Nyandoro , Anton van Wyk

A simple example that I have been requested illustrates the statement in E-print nlin.CD/0201060 that solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent…

Chaotic Dynamics · Physics 2007-05-23 G. Sardanashvily

In this paper the non-canonical Hamiltonian dynamics of a gyrostat in the three body problem will be examined. By means of geometric-mechanics methods some relative equilibria of the dynamics of a gyrostat in Newtonian interaction with two…

Dynamical Systems · Mathematics 2007-05-23 J. A. Vera

We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…

Optimization and Control · Mathematics 2024-09-23 J. J. B. Biemond , R. Postoyan , W. P. M. H. Heemels , N. van de Wouw

We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the…

General Relativity and Quantum Cosmology · Physics 2021-02-24 K. A. Bronnikov , Júlio C. Fabris , Oliver F. Piattella , Denis C. Rodrigues , Edison C. O. Santos

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69…

Plasma Physics · Physics 2010-11-30 Jian-Zhou Zhu , Gregory W. Hammett

The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by…

Quantum Physics · Physics 2009-11-10 P. Van , T. Fulop

A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…

Quantum Physics · Physics 2021-02-02 Elham Jamalinia , Peyman Azodi , Alireza Khayatian , Peyman Setoodeh

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…

Optimization and Control · Mathematics 2020-07-07 Andrii Mironchenko , Christophe Prieur , Fabian Wirth

Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…

Dynamical Systems · Mathematics 2025-05-30 Aaron D. Ames , Sébastien Mattenet , Joe Moeller

The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the concept of partial asymptotic stability and analyzed by…

Optimization and Control · Mathematics 2020-02-07 Victoria Grushkovskaya , Alexander Zuyev

We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…

Analysis of PDEs · Mathematics 2015-02-17 Bruno Premoselli

Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…

Systems and Control · Electrical Eng. & Systems 2021-11-02 A. R. Tavakolpour-Saleh

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…

Systems and Control · Computer Science 2012-06-05 Corentin Briat

In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using…

Classical Analysis and ODEs · Mathematics 2024-09-06 Lamiae Maia , Noha El Khattabi , Marlène Frigon

This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…

Optimization and Control · Mathematics 2022-07-26 Weihai Zhang , Liqiang Yao