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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

We study the dynamical behaviors of this improved memristive neuron model by changing external harmonic current and the magnetic gain parameters. The model shows rich dynamics including periodic and chaotic spiking and bursting, and…

Adaptation and Self-Organizing Systems · Physics 2020-03-03 Marius E. Yamakou

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p $\in$ [2, $\infty$]. Some…

Analysis of PDEs · Mathematics 2019-07-30 Yacine Chitour , Swann Marx , Christophe Prieur

This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the…

Optimization and Control · Mathematics 2012-01-13 Iasson Karafyllis , Zhong-Ping Jiang

We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent…

Dynamical Systems · Mathematics 2014-11-17 Matthew Philippe , Raphaël M. Jungers

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…

Chaotic Dynamics · Physics 2013-07-01 Yian Ma , Ruoshi Yuan , Yang Li , Ping Ao , Bo Yuan

We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a…

Adaptation and Self-Organizing Systems · Physics 2008-02-08 Rui Dilao

This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…

Systems and Control · Electrical Eng. & Systems 2024-04-02 Bing Xiao , Haichao Zhang , Shijie Zhao , Lu Cao

This paper develops a dissipativity-based framework for synthesis of stabilizing controllers for discrete-time nonlinear systems subject to state/input constraints. Firstly, we revisit dissipation inequalities for discrete-time nonlinear…

Optimization and Control · Mathematics 2022-02-23 Mircea Lazar

The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…

Dynamical Systems · Mathematics 2022-04-29 Oskar A. Sultanov

It is well known that, the existence of a Lyapunov function is a sufficient condition for stability, asymptotic stability, or global asymptotic stability of an equilibrium point of an autonomous system $\dot{\mathbf{x}} = f(\mathbf{x})$. In…

Dynamical Systems · Mathematics 2014-05-29 Chirayu D. Athalye , Harish K. Pillai , Debasattam Pal

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…

Systems and Control · Computer Science 2019-03-01 Yohei Hosoe , Tomomichi Hagiwara

A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism…

Chaotic Dynamics · Physics 2009-11-10 Alexey Yu. Jalnine , Andrew H. Osbaldestin

This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9…

Dynamical Systems · Mathematics 2026-01-27 Li Deng , Xin Li

Synergistic hybrid feedback refers to a collection of feedback laws that allow for global asymptotic stabilization of a compact set through the following switching logic: given a collection of Lyapunov functions that are indexed by a logic…

Systems and Control · Electrical Eng. & Systems 2023-01-03 Pedro Casau , Ricardo G. Sanfelice , Carlos Silvestre

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…

Dynamical Systems · Mathematics 2016-11-17 A. N. Gorban , I. Yu. Tyukin , H. Nijmeijer

Recently, a number of counter examples have surfaced where Linear Parameter-Varying (LPV) control synthesis applied to achieve asymptotic output tracking and disturbance rejection for a nonlinear system, fails to achieve the desired…

Systems and Control · Electrical Eng. & Systems 2020-12-10 P. J. W. Koelewijn , G. Sales Mazzoccante , R. Tóth , S. Weiland

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…

Systems and Control · Electrical Eng. & Systems 2020-02-20 Matthew Abate , Corbin Klett , Samuel Coogan , Eric Feron

We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…

Systems and Control · Electrical Eng. & Systems 2021-02-09 Alessandro Abate , Daniele Ahmed , Mirco Giacobbe , Andrea Peruffo

This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…

Dynamical Systems · Mathematics 2025-11-25 Marzieh Basiri Abarghoei , Mohammad Reza Ahmadi Zand