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In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions…

Analysis of PDEs · Mathematics 2023-01-19 Said Kouachi

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

The aim of this paper is to present necessary and sufficient conditions for nonuniform power instability property of linear discrete-time systems in Banach spaces. A characterization of the nonuniform power instability in terms of Lyapunov…

Dynamical Systems · Mathematics 2014-10-03 Ioan-Lucian Popa , Traian Ceausu , Mihail Megan

We prove the necessary and sufficient conditions for practical stability of nonlinear dynamical system at general phase restrictions. In such a case the Lyapunov function is nondifferentiable. But if the set of initial data is starry…

Dynamical Systems · Mathematics 2007-05-23 F. G. Garashchenko , O. M. Bashniakov , V. V. Pichkur

The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety…

Probability · Mathematics 2023-04-18 Marc Arnaudon , Pierre Del Moral , El Maati Ouhabaz

Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high…

Systems and Control · Electrical Eng. & Systems 2020-06-16 Wenxin Xiao , Armin Lederer , Sandra Hirche

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

Probability · Mathematics 2023-05-22 Taras Lukashiv , Igor V. Malyk , Maryna Chepeleva , Petr V. Nazarov

It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the…

Dynamical Systems · Mathematics 2013-08-05 Samuel Coogan , Murat Arcak

An approach for computing Lyapunov functions for nonlinear continuous-time differential equations is developed via a new, Massera-type construction. This construction is enabled by imposing a finite-time criterion on the integrated…

Dynamical Systems · Mathematics 2016-09-16 Alina I. Doban , Mircea Lazar

We investigate the uniform stability properties of discrete-time linear switched systems subject to arbitrary switching, focusing on the "marginally unstable" regime in which the system is not Lyapunov stable but in which trajectories…

Dynamical Systems · Mathematics 2022-03-28 Ian D. Morris

We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…

Systems and Control · Electrical Eng. & Systems 2022-07-15 Adrien Banse , Zheming Wang , Raphaël M. Jungers

Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth --…

Optimization and Control · Mathematics 2022-11-08 Pavel Osinenko , Grigory Yaremenko , Georgiy Malaniya

For discrete-time systems, governed by Kraus maps, the work of D. Petz has characterized the set of universal contraction metrics. In the present paper, we use this characterization to derive a set of quadratic Lyapunov functions for…

Optimization and Control · Mathematics 2013-02-28 Pierre Rouchon , Alain Sarlette

In this paper we consider an SIRS epidemic model under a general assumption of density-dependent mortality. We prove the global stability of the disease-free equilibrium and propose a Lyapunov function that allows to demonstrate the global…

Dynamical Systems · Mathematics 2018-12-31 Alberto d'Onofrio , Piero Manfredi , Ernesto Salinelli

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

Empirically defining some constant probabilistic orbits of f(x) and g(x) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open…

Chaotic Dynamics · Physics 2019-11-19 Charles Roberto Telles

A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…

Systems and Control · Electrical Eng. & Systems 2023-09-12 Reynaldo Ortiz , Alexey Egorov , Sabine Mondié

Motivated by the Lyapunov convexity theorem in infinite dimensions, we extend the convexity of the integral of a decomposable set to separable Banach spaces under the strengthened notion of nonatomicity of measure spaces, called…

Functional Analysis · Mathematics 2019-03-12 Nobusumi Sagara

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''.…

Dynamical Systems · Mathematics 2007-05-23 A. Chaillet , A. Loria

In this paper a nonlinear Euler-Poisson-Darboux system is considered. In a first part, we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel…

Analysis of PDEs · Mathematics 2017-05-02 Anouar Ben Mabrouk