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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

In recent years, attempts have been made to extend nonlinear small-gain theorems for input-to-state stability (ISS) from finite networks to countably infinite networks with finite indegrees. Under specific assumptions about the…

Optimization and Control · Mathematics 2026-01-27 Christoph Kawan

For an ISS system, by analyzing local and non-local properties, it is obtained different input-to-state gains. The interconnection of a system having two input-to-state gains with a system having a single ISS gain is analyzed. By employing…

Optimization and Control · Mathematics 2015-08-12 Humberto Stein Shiromoto , Vincent Andrieu , Christophe Prieur

We consider the interconnections of arbitrary topology of a finite number of ISS hybrid systems and study whether the ISS property is maintained for the overall system. We show that if the small gain condition is satisfied, then the whole…

Dynamical Systems · Mathematics 2012-02-28 Sergey Dashkovskiy , Michael Kosmykov

We derive converse Lyapunov theorems for input-to-state stability (ISS) of linear infinite-dimensional analytic systems. We show that input-to-state stability of a linear system does not imply existence of a coercive quadratic ISS Lyapunov…

Optimization and Control · Mathematics 2025-09-19 Andrii Mironchenko , Felix Schwenninger

Input-to-state stability (ISS) of switched systems is studied where the individual subsystems are connected in a serial cascade configuration, and the states are allowed to reset at switching times. An ISS Lyapunov function is associated to…

Systems and Control · Computer Science 2020-01-07 GuangXue Zhang , Aneel Tanwani

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

A notion of "asymptotic Cauchy gain" for input/output systems, and an associated small-gain principle, are introduced. A Lyapunov-like characterization allows the computation of these gains for state-space systems, and the formulation of…

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

We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a…

Optimization and Control · Mathematics 2026-04-14 Yassine El Gantouh , Jun Zheng , Guchuan Zhu , Dingshi Li

The present work provides two alternatives to formulate time-discounted incremental input/output-to-state stability (i-IOSS) as a suitable detectability notion for general nonlinear systems with non-additive disturbances. Both formulations…

Systems and Control · Electrical Eng. & Systems 2020-05-01 Sven Knuefer , Matthias A. Mueller

This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonlinear dynamical systems is introduced, along with its…

Optimization and Control · Mathematics 2025-07-04 Leilei Cui , Zhong-Ping Jiang , Eduardo D. Sontag , Richard D. Braatz

Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This note provides…

Systems and Control · Computer Science 2017-02-02 H. Haimovich , J. L. Mancilla-Aguilar

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 introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork, while it allows for non-uniform convergence of all components. For an…

Optimization and Control · Mathematics 2021-07-29 Andrii Mironchenko

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

Optimization and Control · Mathematics 2012-12-24 Sergey Dashkovskiy , Andrii Mironchenko

Convergent, contractive or incremental stability properties of nonlinear systems have attracted interest for control tasks such as observer design, output regulation and synchronization. The convergence property plays a central role in the…

Systems and Control · Electrical Eng. & Systems 2021-05-07 Jiayen Chen , Hendra I. Nurdin

This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability ($\delta$-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown system dynamics, we…

Systems and Control · Electrical Eng. & Systems 2025-01-13 Ahan Basu , Bhabani Shankar Dey , Pushpak Jagtap

In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…

Optimization and Control · Mathematics 2018-09-17 Nicoletta Bof , Ruggero Carli , Luca Schenato

We provide a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a recent small-gain theorem of Angeli and Sontag for monotone systems with…

Optimization and Control · Mathematics 2007-05-23 Michael Malisoff , Patrick de Leenheer

It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to…

Systems and Control · Electrical Eng. & Systems 2021-09-01 José L. Mancilla-Aguilar , Hernan Haimovich