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In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of…

Dynamical Systems · Mathematics 2015-11-25 Roman Geiselhart , Fabian R. Wirth

A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…

Systems and Control · Electrical Eng. & Systems 2022-02-14 Lars Grüne , Thomas Meurer

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

We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a…

Analysis of PDEs · Mathematics 2014-07-18 Serge Nicaise , Cristina Pignotti

In this paper, first, it is shown that if a nonlinear time-varying system is contractive, then it is incrementally exponentially stable. Second, leveraging this result, under mild restrictions, an approach is proposed to design feedforward…

Systems and Control · Electrical Eng. & Systems 2025-03-31 Mohamed Yassine Arkhis , Denis Efimov

In this work we consider linear non-autonomous systems of Wazewski type on Hilbert spaces and provide a new approach to study their stability properties by means of a decomposition into subsystems and conditions implied on the…

Dynamical Systems · Mathematics 2025-03-13 Ivan Atamas , Sergey Dashkovskiy , Vitalii Slynko

This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…

Optimization and Control · Mathematics 2020-05-14 Steffi Knorn , Bart Besselink

The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly…

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

The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…

Optimization and Control · Mathematics 2018-09-24 Matthieu Barreau , Frédéric Gouaisbaut , Alexandre Seuret , Rifat Sipahi

This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…

Optimization and Control · Mathematics 2021-05-13 Qishu Yan , Huaiqiang Yu

We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a…

Optimization and Control · Mathematics 2021-05-07 John W. Simpson-Porco

The increasing share of converter based resources in power systems calls for scalable methods to analyse stability without relying on exhaustive system wide simulations. Decentralized small gain and small-phase criteria have recently been…

Systems and Control · Electrical Eng. & Systems 2026-04-15 Diego Cifelli , Adolfo Anta

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to…

Optimization and Control · Mathematics 2010-09-13 Sergey N. Dashkovskiy , Björn S. Rüffer , Fabian R. Wirth

Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…

Optimization and Control · Mathematics 2022-11-15 Saman Cyrus , Laurent Lessard

Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI)…

Systems and Control · Electrical Eng. & Systems 2023-11-21 Sei Zhen Khong , Di Zhao , Alexander Lanzon

It is often of interest to know which systems will approach a periodic trajectory when given a periodic input. Results are available for certain classes of systems, such as contracting systems, showing that they always entrain to periodic…

Optimization and Control · Mathematics 2023-10-06 Alon Duvall , Eduardo Sontag

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for…

Optimization and Control · Mathematics 2007-05-23 Lars Grüne , Eduardo D. Sontag , Fabian R. Wirth

We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is…

Analysis of PDEs · Mathematics 2018-06-28 Robert Denk , Felix Kammerlander

Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional…

Systems and Control · Electrical Eng. & Systems 2024-06-05 Andrii Mironchenko , Christophe Prieur

This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems.…

Systems and Control · Computer Science 2016-11-28 Sérgio Waitman , Paolo Massioni , Laurent Bako , Gérard Scorletti , Vincent Fromion