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The aggressive integration of distributed renewable sources is changing the dynamics of the electric power grid in an unexpected manner. As a result, maintaining conventional performance specifications, such as transient stability, may not…

Optimization and Control · Mathematics 2018-06-14 Liviu Aolaritei , Dongchan Lee , Thanh Long Vu , Konstantin Turitsyn

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

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…

Optimization and Control · Mathematics 2026-03-05 Patrick Bachmann , Andrii Mironchenko

In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS…

Systems and Control · Electrical Eng. & Systems 2026-03-06 Saeed Ahmed , Patrick Bachmann , Stephan Trenn

Since the concept of input-to-state stability (ISS) was introduced, it has been extensively investigated for finite-dimensional control systems and has recently received attention for infinite-dimensional systems. While numerical techniques…

Optimization and Control · Mathematics 2026-03-03 Birgit Hillebrecht , Benjamin Unger

The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function is, however, nothing else than a squared Euclidean norm on the…

Optimization and Control · Mathematics 2024-01-17 Anton V. Proskurnikov , Alexander Davydov , Francesco Bullo

In this paper, we provide a novel solution to an open problem on the global uniform stability of switched nonlinear systems. Our results are based on the Koopman operator approach and, to our knowledge, this is the first theoretical…

Dynamical Systems · Mathematics 2024-03-06 Christian Mugisho Zagabe , Alexandre Mauroy

Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…

Systems and Control · Electrical Eng. & Systems 2025-11-12 Tessina H. Scholl

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

Optimization and Control · Mathematics 2016-11-09 Corentin Briat

The paper introduces sufficient conditions for input-to-state stability (ISS) of a class of impulsive systems with jump maps that depend on time. Such systems can naturally represent an interconnection of several impulsive systems with…

Systems and Control · Computer Science 2016-05-30 Sergey Dashkovskiy , Petro Feketa

Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to…

Optimization and Control · Mathematics 2015-05-26 Iasson Karafyllis , Miroslav Krstic

Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…

Optimization and Control · Mathematics 2021-03-08 Dimitris Kousoulidis , Fulvio Forni

By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide…

Optimization and Control · Mathematics 2024-10-01 T. J. Meijer , V. S. Dolk , W. P. M. H. Heemels

This paper studies input-to-state stability (ISS) of general nonlinear time-delay systems subject to delay-dependent impulse effects. Sufficient conditions for ISS are constructed by using the method of Lyapunov functionals. It is shown…

Optimization and Control · Mathematics 2022-06-09 Xinzhi Liu , Kexue Zhang

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

This paper deals with several related notions of output stability with respect to inputs. The inputs may be thought of as disturbances; when there are no inputs, one obtains generalizations of the classical concepts of partial stability.…

Optimization and Control · Mathematics 2007-05-23 Eduardo D. Sontag , Y. Wang

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the…

Optimization and Control · Mathematics 2022-05-17 Iasson Karafyllis , Pierdomenico Pepe , Yuan Wang , Antoine Chaillet

This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…

Optimization and Control · Mathematics 2022-07-26 Weihai Zhang , Liqiang Yao

This paper tackles state feedback control of switched linear systems under arbitrary switching. We propose a data-driven control framework that allows to compute a stabilizing state feedback using only a finite set of observations of…

Optimization and Control · Mathematics 2022-05-05 Zheming Wang , Guillaume O. Berger , Raphaël M. Jungers

Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…

Systems and Control · Electrical Eng. & Systems 2025-10-01 Michael Tang , Miroslav Krstic , Jorge Poveda