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Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…

Machine Learning · Computer Science 2025-12-22 Guner Dilsad Er , Sebastian Trimpe , Michael Muehlebach

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

Dynamical Systems · Mathematics 2013-06-12 A. Gorban , I. Tyukin , E. Steur , H. Nijmeijer

Title: Global stabilization of control nonlinear system "inverted pendulum on a cart" using method of two Lyapunov functions Authors: B. L. Mazov (Nizhny Novgorod Technical University) Comments: 10 pages Subj-class: Dynamical Systems…

Dynamical Systems · Mathematics 2007-05-23 B. L. Mazov

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

Optimization and Control · Mathematics 2018-11-06 Duc N. Tran , Björn S. Rüffer , Christopher M. Kellett

Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…

Systems and Control · Electrical Eng. & Systems 2022-10-18 Ruikun Zhou , Thanin Quartz , Hans De Sterck , Jun Liu

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 book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…

Optimization and Control · Mathematics 2024-04-09 Qian Feng , Alexandre Seuret , Sing Kiong Nguang

This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to…

Optimization and Control · Mathematics 2018-10-11 Qifeng Li , Konstantin Turitsyn

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…

Dynamical Systems · Mathematics 2007-05-23 Ivan Tyukin , Erik Steur , Henk Nijmeijer , Cees van Leeuwen

We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…

Optimization and Control · Mathematics 2025-10-10 Hassan Saoud

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

For a pendulum suspended below a vibrating block with white noise forcing, the solution in which the pendulum remains vertical is called the single mode solution. When this solution becomes unstable there is energy transfer from the block…

Probability · Mathematics 2023-02-07 Peter H. Baxendale , N. Sri Namachchivaya

Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…

Systems and Control · Computer Science 2017-11-01 Thanh Long Vu , Konstantin Turitsyn

Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine…

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

There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…

Systems and Control · Electrical Eng. & Systems 2024-02-15 Jongrae Kim

Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…

Robotics · Computer Science 2024-05-14 Yu Zhang , Yongxiang Zou , Haoyu Zhang , Xiuze Xia , Long Cheng

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…

Optimization and Control · Mathematics 2007-05-23 Frederic Mazenc , Michael Malisoff , Marcio S. de Queiroz

Unlike ordinary differential equations (ODEs), linear partial differential equations (PDEs) admit multiple non-equivalent notions of stability. This variety makes interpretation of Lyapunov stability results challenging. \blue{To simplify…

Optimization and Control · Mathematics 2026-05-26 Matthew M. Peet

This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous- and discrete-time cases. The sufficient conditions for the existence and uniqueness of a…

Optimization and Control · Mathematics 2015-09-04 Yong Zhao , Weihai Zhang

This work studies robustness to system disturbance and measurement noise of some popular general practical stabilization techniques, namely, Dini aiming, optimization-based stabilization and inf-convolution stabilization. Common to all…

Systems and Control · Electrical Eng. & Systems 2025-03-14 Patrick Schmidt , Pavel Osinenko , Stefan Streif