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Related papers: Input / Output Stability of a Damped String Equati…

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In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…

Dynamical Systems · Mathematics 2025-04-03 Wataru Saito , Ikki Fukuda

We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…

Dynamical Systems · Mathematics 2019-07-04 Stefan Siegmund , Petr Stehlik

Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional…

Systems and Control · Electrical Eng. & Systems 2024-06-05 Andrii Mironchenko , Christophe Prieur

Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…

Logic in Computer Science · Computer Science 2022-02-25 Yong Kiam Tan , André Platzer

This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…

Optimization and Control · Mathematics 2016-03-14 Filip Koerts , Mathias Bürger , Arjan van der Schaft , Claudio De Persis

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

In this paper we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belonging to $L^1_{loc}([0, +\infty)).$ Under suitable assumptions, we show…

Analysis of PDEs · Mathematics 2021-08-31 Alessandro Paolucci , Cristina Pignotti

This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…

Classical Analysis and ODEs · Mathematics 2026-03-27 John A. D. Appleby , Subham Pal

Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability…

Optimization and Control · Mathematics 2022-08-31 Hasala Gallolu Kankanamalage , Yuandan Lin , Yuan Wang

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…

Analysis of PDEs · Mathematics 2007-05-23 M. I. Caiado , A. V. Sarychev

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Machine Learning · Computer Science 2024-03-04 Igor Pontes Duff , Pawan Goyal , Peter Benner

In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…

Analysis of PDEs · Mathematics 2023-07-28 Shijie Zhou , Hongyinping Feng , Zhiqiang Wang

We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…

Functional Analysis · Mathematics 2025-04-01 Serge Nicaise , Lassi Paunonen , David Seifert

This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…

Analysis of PDEs · Mathematics 2019-04-25 Matthieu Barreau , Alexandre Seuret , Frédéric Gouaisbaut , Lucie Baudouin

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

Probability · Mathematics 2018-10-25 Leonid Shaikhet

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

Dynamical Systems · Mathematics 2017-08-18 Bin Zhou

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

In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…

Dynamical Systems · Mathematics 2007-05-23 Iasson Karafyllis , Pierdomenico Pepe , Zhong-Ping Jiang

We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…

Analysis of PDEs · Mathematics 2023-11-30 Thierry Goudon , Simona Rota Nodari

A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…

Systems and Control · Electrical Eng. & Systems 2022-02-14 Lars Grüne , Thomas Meurer