English
Related papers

Related papers: Converse Lyapunov theorems for discrete-time linea…

200 papers

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…

Probability · Mathematics 2008-07-10 Bernard Bercu , Francois Dufour , G. George Yin

In this work, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of…

Optimization and Control · Mathematics 2021-01-12 Irina Subotić , Dominic Groß , Marcello Colombino , Florian Dörfler

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

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…

Optimization and Control · Mathematics 2012-05-18 Serdar Yüksel , Sean P. Meyn

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different…

Optimization and Control · Mathematics 2015-08-25 Nikolaos Bekiaris-Liberis , Miroslav Krstic

The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…

Dynamical Systems · Mathematics 2017-11-07 Rachid Bouyekhf , Lyubomir T. Gruyitch

This paper studies the cooperative global robust stabilization problem for a class of nonlinear multi-agent systems. The problem is motivated from the study of the cooperative global robust output regulation problem for the class of…

Optimization and Control · Mathematics 2015-08-20 Wei Liu , Jie Huang

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Dynamical Systems · Mathematics 2022-06-10 Giovanni Russo , Fabian Wirth

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…

Optimization and Control · Mathematics 2018-06-25 Tianliang Zhang , Feiqi Deng , Weihai Zhang

An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing…

Dynamical Systems · Mathematics 2022-07-27 Sabine Mondié , Alexey Egorov , Marco A. Gomez

Lyapunov's second or direct method is one of the most widely used techniques for investigating stability properties of dynamical systems. This technique makes use of an auxiliary function, called a Lyapunov function, to ascertain stability…

Optimization and Control · Mathematics 2016-08-12 Christopher M. Kellett

Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…

Optimization and Control · Mathematics 2023-10-03 Corentin Briat

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

Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic…

Optimization and Control · Mathematics 2024-10-02 Martin Gugat

We study the well known Schr\"odinger-Lohe model for quantum synchronization with non-identical natural frequencies. The main results are related to the characterization and convergence to phase-locked states for this quantum system. The…

Analysis of PDEs · Mathematics 2024-12-31 Paolo Antonelli , David N Reynolds

In this paper, we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, which includes…

Optimization and Control · Mathematics 2021-09-10 Anna Chiara Lai , Monica Motta

Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…

Dynamical Systems · Mathematics 2025-08-01 Aaron D. Ames , Joe Moeller , Paulo Tabuada

Learned models and policies can generalize effectively when evaluated within the distribution of the training data, but can produce unpredictable and erroneous outputs on out-of-distribution inputs. In order to avoid distribution shift when…

Machine Learning · Computer Science 2022-06-22 Katie Kang , Paula Gradu , Jason Choi , Michael Janner , Claire Tomlin , Sergey Levine

This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two…

Systems and Control · Electrical Eng. & Systems 2026-02-09 Antonio Russo , Gian Paolo Incremona , Patrizio Colaneri

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