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This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we…

Analysis of PDEs · Mathematics 2022-11-07 S. Dashkovskiy , O. Kapustyan , V. Slynko

This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…

Optimization and Control · Mathematics 2021-03-09 Matthieu Barreau , Sophie Tarbouriech , Frederic Gouaisbaut

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

Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…

Systems and Control · Electrical Eng. & Systems 2022-07-19 Konstantin Zimenko , Denis Efimov , Andrey Polyakov

The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…

Dynamical Systems · Mathematics 2023-02-14 Wenjie Hu , Quanxin Zhu , Tomás Caraballo

In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…

Systems and Control · Electrical Eng. & Systems 2025-05-30 Chaimae El Mortajinea , Moussa Labbadib , Adnane Saoudc , Mostafa Bouzia

We consider finite-dimensional systems of linear stochastic differential equations ${\partial_t}{x_k}\left( t \right) = {A_{kp}}\left( t \right){x_p}\left( t \right)$, ${\bf A}(t)$ being a stationary continuous statistically isotropic…

Probability · Mathematics 2023-10-26 A. S. Il'yn , A. V. Kopyev , V. A. Sirota , K. P. Zybin

This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…

Optimization and Control · Mathematics 2014-03-25 Iasson Karafyllis , Markos Papageorgiou

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…

Optimization and Control · Mathematics 2007-05-23 Frederic Mazenc , Michael Malisoff

A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…

Systems and Control · Electrical Eng. & Systems 2021-01-28 He Yin , Peter Seiler , Murat Arcak

In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on…

Systems and Control · Electrical Eng. & Systems 2021-09-22 Hassan Abdelraouf , Fahad Albalawi , Eric Feron

Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…

Systems and Control · Electrical Eng. & Systems 2020-12-08 Corbin Klett , Matthew Abate , Samuel Coogan , Eric Feron

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…

Chaotic Dynamics · Physics 2009-10-20 Roberto Artuso , Cesar Manchein

A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results…

Optimization and Control · Mathematics 2021-10-13 Marc Artola , Charlotte Rodriguez , Andrew Wynn , Rafael Palacios , Günter Leugering

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…

chao-dyn · Physics 2009-10-31 Awadhesh Prasad , Ramakrishna Ramaswamy

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…

Machine Learning · Computer Science 2026-03-18 Hiroyasu Tsukamoto , Soon-Jo Chung , Jean-Jacques E. Slotine

We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…

Optimization and Control · Mathematics 2025-09-03 Hoang Huy Nguyen , Siva Theja Maguluri

This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…

Optimization and Control · Mathematics 2024-04-09 Qian Feng , Alexandre Seuret , Sing Kiong Nguang

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

The problem of domain aiming control is formulated for controlled stochastic nonlinear systems. This issue involves regularity of the solution to the resulting closed-loop stochastic system. To begin with, an extended existence and…

Optimization and Control · Mathematics 2018-11-15 Juliang Yin , Deng Ding , Suiyang Khoo