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Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis

While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…

Systems and Control · Electrical Eng. & Systems 2024-03-18 Jun Liu , Yiming Meng , Maxwell Fitzsimmons , Ruikun Zhou

In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for stability verification of stochastic systems. Weaker…

Dynamical Systems · Mathematics 2017-02-20 Umesh Vaidya

Dwell-time based stability conditions for a class of LPV systems with piecewise constant parameters under time-varying delay are derived using clock-dependent Lyapunov-Krasovskii functional. Sufficient synthesis conditions for…

Systems and Control · Electrical Eng. & Systems 2020-03-11 Muhammad Zakwan , Saeed Ahmed

Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…

Dynamical Systems · Mathematics 2016-09-26 Soumya Kundu , Marian Anghel

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…

Systems and Control · Electrical Eng. & Systems 2023-07-07 A. M. Zenkin , A. A. Peregudin , A. A. Bobtsov

In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…

Optimization and Control · Mathematics 2014-09-01 Amit Diwadkar , Umesh Vaidya

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…

Functional Analysis · Mathematics 2012-06-26 A. G. Ramm , V. Volpert

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…

Dynamical Systems · Mathematics 2023-08-11 Vitalii Slynko , Sergey Dashkovskiy , Ivan Atamas

In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of…

Optimization and Control · Mathematics 2025-05-20 Annika Fürnsinn , Christian Ebenbauer , Bahman Gharesifard

In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…

Analysis of PDEs · Mathematics 2018-08-17 Swann Marx , Yacine Chitour , Christophe Prieur

We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for…

Systems and Control · Electrical Eng. & Systems 2024-01-25 Hassan Abdelraouf , Eric Feron , Jeff S. Shamma

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Dynamical Systems · Mathematics 2007-07-03 Matthew M. Peet , Antonis Papachristodoulou , Sanjay Lall

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

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…

Machine Learning · Computer Science 2025-11-13 Tomoki Koike , Elizabeth Qian

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…

Classical Analysis and ODEs · Mathematics 2010-09-16 Antonio Canada , Salvador Villegas

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…

Chaotic Dynamics · Physics 2009-11-13 F. Ginelli , P. Poggi , A. Turchi , H. Chaté , R. Livi , A. Politi

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

In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…

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

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

Systems and Control · Electrical Eng. & Systems 2022-08-12 Francesco Ferrante , Giorgio Valmorbida