English
Related papers

Related papers: Contraction Theory for Nonlinear Stability Analysi…

200 papers

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…

Optimization and Control · Mathematics 2024-09-12 Matteo Tacchi , Yingzhao Lian , Colin Jones

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…

Systems and Control · Computer Science 2018-05-09 Zahra Aminzare , Biswadip Dey , Elizabeth N. Davison , Naomi Ehrich Leonard

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

Optimization and Control · Mathematics 2007-05-23 Tyukin Ivan , Danil Prokhorov , Cees van Leeuwen

This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…

Systems and Control · Electrical Eng. & Systems 2026-03-10 Rihan Aaron D'Silva , Hiroyasu Tsukamoto

We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…

Dynamical Systems · Mathematics 2025-07-10 Pascal Stiefenhofer

Driven by the flexible manufacturing trend in the process control industry and the uncertain nature of chemical process models, this article aims to achieve offset-free tracking for a family of uncertain nonlinear systems (e.g., using…

Systems and Control · Electrical Eng. & Systems 2022-05-10 Lai Wei , Ryan McCloy , Jie Bao

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…

Optimization and Control · Mathematics 2022-08-02 Alexander Davydov , Saber Jafarpour , Francesco Bullo

We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…

Systems and Control · Electrical Eng. & Systems 2020-10-06 Saber Jafarpour , Pedro Cisneros-Velarde , Francesco Bullo

The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is…

Dynamical Systems · Mathematics 2019-09-24 Peter Giesl , Sigurdur Hafstein , Iman Mehrabinezhad

Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…

Optimization and Control · Mathematics 2022-02-02 Pedro Cisneros-Velarde , Francesco Bullo

This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…

Dynamical Systems · Mathematics 2007-05-23 Matthew M. Peet

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

Optimization and Control · Mathematics 2021-06-07 Pedro Cisneros-Velarde , Saber Jafarpour , Francesco Bullo

In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…

Systems and Control · Computer Science 2019-03-11 Me Le , Chi Yanxun , Li Zhiwei , Xu Dongfu , Zhang Yulong

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

Dynamical Systems · Mathematics 2017-08-18 Bin Zhou

This paper presents a modular framework for motion planning using movement primitives. Central to the approach is Contraction Theory, a modular stability tool for nonlinear dynamical systems. The approach extends prior methods by achieving…

Robotics · Computer Science 2025-01-17 Moses C. Nah , Johannes Lachner , Neville Hogan , Jean-Jacques Slotine

Nonlinear robust control is pursued by overcoming the drawback of linear robust control that it ignores available information about existing nonlinearities and the resulting controllers may be too conservative, especially when the…

Systems and Control · Electrical Eng. & Systems 2019-12-30 Yongqiang Li , Chaolun Lu , Zhongsheng Hou , Yuanjing Feng

A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…

Optimization and Control · Mathematics 2021-09-29 Chengshuai Wu , Ilya Kanevskiy , and Michael Margaliot

Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…

Systems and Control · Electrical Eng. & Systems 2025-11-17 Adel Bechihi , Aristotelis Kapnopoulos

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…

Dynamical Systems · Mathematics 2015-05-20 Giovanni Russo , Jean-Jacques E. Slotine

This paper develops an adaptive tracking controller for a class of nonlinear systems with parametric uncertainty subject to state constraints. The system is characterized by a strict-feedback structure with unknown parameters entering both…

Optimization and Control · Mathematics 2026-04-29 Jhon Manuel Portella Delgado , Ankit Goel