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Related papers: Input-to-state stability of infinite-dimensional s…

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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

We develop a Lyapunov-based small-gain theorem for establishing fixed-time input-to-state stability (FxT-ISS) guarantees in interconnected nonlinear dynamical systems. The proposed framework considers interconnections in which each…

Systems and Control · Electrical Eng. & Systems 2025-12-25 Michael Tang , Miroslav Krstic , Jorge Poveda

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations…

Optimization and Control · Mathematics 2017-09-21 Andrii Mironchenko , Fabian Wirth

This paper is devoted to two issues. One is to provide Lyapunov-based tools to establish integral input-to-state stability (iISS) and input-to-state stability (ISS) for some classes of nonlinear parabolic equations. The other is to provide…

Dynamical Systems · Mathematics 2014-10-14 Andrii Mironchenko , Hiroshi Ito

Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…

Systems and Control · Electrical Eng. & Systems 2023-05-01 Preston Culbertson , Ryan K. Cosner , Maegan Tucker , Aaron D. Ames

We prove a superposition theorem for input-to-output stability (IOS) of a broad class of nonlinear infinite-dimensional systems with outputs including both continuous-time and discrete-time systems. It contains, as a special case, the…

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

Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects…

Optimization and Control · Mathematics 2022-03-09 Felix Schwenninger

For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral input-to-state stability. We provide two proofs of this fact. One applies to general systems over Banach…

Dynamical Systems · Mathematics 2019-05-08 Andrii Mironchenko , Hiroshi Ito

We prove that impulsive systems, which possess an ISS Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which…

Dynamical Systems · Mathematics 2012-12-24 Sergey Dashkovskiy , Andrii Mironchenko

We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In…

Optimization and Control · Mathematics 2025-10-17 Rahma Heni , Andrii Mironchenko , Fabian Wirth , Hanen Damak , Mohamed Ali Hammami

At the occasion of Eduardo D. Sontag's 70 th birthday, we provide here an overview of the tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation of the…

Optimization and Control · Mathematics 2022-06-14 Antoine Chaillet , Iasson Karafyllis , Pierdomenico Pepe , Yuan Wang

We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…

Optimization and Control · Mathematics 2007-05-23 Michael Malisoff , Frederic Mazenc

The study proposes new results on the set input-to-state stability (ISS) subject to a small input time delay for compact, invariant sets that contains the origin. First, using the nonlinear small-gain theory, we prove a Razumikhin-type…

Systems and Control · Electrical Eng. & Systems 2022-11-24 Pallavi Sinha , Irinel-Constantin Morărescu , Sukumar Srikant

We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that…

Optimization and Control · Mathematics 2017-08-29 Andrii Mironchenko , Fabian Wirth

This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory…

Systems and Control · Electrical Eng. & Systems 2026-04-24 Wenbang Wang , Neng Li , Wei Ren

In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function,…

Optimization and Control · Mathematics 2020-11-09 Simone Göttlich , Michael Herty , Gediyon Weldegiyorgis

This paper develops a neural network based control framework that ensures system safety and input-to-state stability (ISS) for general nonlinear switched systems with unknown dynamics. Leveraging the concept of dwell time, we derive…

Systems and Control · Electrical Eng. & Systems 2026-01-22 Bhabani Shankar Dey , Ahan Basu , Pushpak Jagtap

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

A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to…

Optimization and Control · Mathematics 2007-05-23 Brian Ingalls , Eduardo D. Sontag

In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prove an FTISS Lyapunov theorem for a class of…

Optimization and Control · Mathematics 2024-08-21 Xiaorong Sun , Jun Zheng , Guchuan Zhu