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Related papers: Lyapunov-Razumikhin techniques for state-dependent…

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We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is…

Analysis of PDEs · Mathematics 2023-07-11 Shanshan Wang , Jie Qi , Miroslav Krstic

This paper studies the stabilization and safety problems of nonlinear time-delay systems, where time delays exist in system state and affect the controller design. Following the Razumikhin approach, we propose a novel control…

Systems and Control · Electrical Eng. & Systems 2021-09-28 Wei Ren

This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence of Dirichlet-Robin boundary disturbances, as well as…

Optimization and Control · Mathematics 2026-02-11 Yongchun Bi , Jun Zheng , Guchuan Zhu

We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.

Classical Analysis and ODEs · Mathematics 2010-08-05 Claudio Cuevas , Miguel V. S. Frasson

In this paper, we introduce for the first time a class of state-dependent maximal monotone differential inclusions. Then the existence and uniqueness of solutions are obtained by using an implicit discretization scheme and a kind of…

Optimization and Control · Mathematics 2019-03-06 Ba Khiet Le

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…

Analysis of PDEs · Mathematics 2018-12-12 Lucie Baudouin , Alexandre Seuret , Frédéric Gouaisbaut

This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows…

Probability · Mathematics 2025-07-01 Dan Noelck

In this work we study the asymptotic behavior of a class of damped second-order gradient systems $$ \ddot{u}(t) + a\dot{u}(t) + \nabla W(u(t)) = 0, $$ under assumptions ensuring local convexity of the potential near equilibrium and…

Classical Analysis and ODEs · Mathematics 2025-12-25 Renan J. S. Isneri , Eric B. Santiago , Severino H. da Silva

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…

Classical Analysis and ODEs · Mathematics 2018-07-10 Teresa Faria , Rafael Obaya , Ana M. Sanz

This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…

Analysis of PDEs · Mathematics 2017-10-11 Kaïs Ammari , Boumediène Chentouf

We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of several physical processes, where small delay effects are…

Dynamical Systems · Mathematics 2021-08-13 Jiaqi Yang , Joan Gimeno , Rafael de la Llave

We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay,…

Systems and Control · Electrical Eng. & Systems 2025-01-28 Florent Koudohode , Nikolaos Bekiaris-Liberis

We consider an interlinked production model consisting of conservation laws (PDE) coupled to ordinary differential equations (ODE). Our focus is the analysis of control laws for the coupled system and corresponding stabilization questions…

Optimization and Control · Mathematics 2019-12-13 Vanessa Baumgärtner , Simone Göttlich , Stephan Knapp

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 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

This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to…

Optimization and Control · Mathematics 2018-10-11 Qifeng Li , Konstantin Turitsyn

This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…

Dynamical Systems · Mathematics 2026-05-14 Teresa Faria , Anatoliy A. Martynyuk

Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…

The analysis of the stability of systems' equilibria plays a central role in the study of dynamical systems and control theory. This note establishes an extension of the celebrated Krasovski\u{\i} stability theorem for functional…

Optimization and Control · Mathematics 2025-07-08 Qian Feng , Wilfrid Perruquetti

In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…

Optimization and Control · Mathematics 2016-03-28 Evgeny Meyer , Matthew M. Peet