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Related papers: Input-to-state stability meets small-gain theory

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The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…

Systems and Control · Electrical Eng. & Systems 2020-05-29 Fabio Bonassi , Enrico Terzi , Marcello Farina , Riccardo Scattolini

We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs.…

Optimization and Control · Mathematics 2018-08-22 Andrii Mironchenko , Iasson Karafyllis , Miroslav Krstic

This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed…

Optimization and Control · Mathematics 2021-08-18 Hugo Lhachemi , David Saussié , Guchuan Zhu , Robert Shorten

This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most recent work of Marcondes de Freitas and Sontag \cite{FS3}, we…

Dynamical Systems · Mathematics 2016-08-23 Jifa Jiang , Xiang Lv

Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a…

Quantitative Methods · Quantitative Biology 2007-05-23 David Angeli , 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

Achieving control objectives (e.g., stabilization or convergence of tracking error to zero, input-to-state stabilization) in "prescribed time" has attracted significant research interest in recent years. The key property of prescribed-time…

Optimization and Control · Mathematics 2024-05-02 Prashanth Krishnamurthy , Farshad Khorrami , Anthony Tzes

This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equations (PDEs) with different types of boundary disturbances…

Analysis of PDEs · Mathematics 2020-06-24 Jun Zheng , Guchuan Zhu

This paper presents a systematic method to analyze stability and robustness of uncertain Quantum Input-Output Networks (QIONs). A general form of uncertainty is introduced into quantum networks in the SLH formalism. Results of this paper…

Quantum Physics · Physics 2021-03-04 Peyman Azodi , Alireza Khayatian , Peyman Setoodeh

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

This paper studies distributed adaptive estimation over sensor networks with partially unknown source dynamics. We present parallel continuous-time and discrete-time designs in which each node runs a local adaptive observer and exchanges…

Systems and Control · Electrical Eng. & Systems 2026-05-18 Moh Kamalul Wafi , Hamidreza Montazeri Hedesh , Milad Siami

A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an…

Optimization and Control · Mathematics 2020-06-09 Mapundi Kondwani Banda , Gediyon Weldegiyorgis

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…

Optimization and Control · Mathematics 2016-11-17 Daniel Liberzon , A. Stephen Morse , Eduardo D. Sontag

We extend the results of the general small-gain theorem proposed by Z.P Jiang. The significance of this extension is two fold. First, it allows one to use general vector norm to characterize the input-to-output property of two…

Systems and Control · Computer Science 2014-09-25 Yunsheng Li , Chi Jin

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…

Systems and Control · Computer Science 2012-06-05 Corentin Briat

A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…

Optimization and Control · Mathematics 2025-01-28 Andrii Mironchenko

Stability is a very important property of any physical system. By a stable system, we broadly mean that small disturbances either in the system inputs or in the initial conditions do not lead to large changes in the overall behavior of the…

Information Theory · Computer Science 2013-02-27 Ratnadip Adhikari

Stability is a critical feature of distributed linear multi-input-multi-output systems. Global asymptotic stability usually can be guaranteed when using decentralised or distributed control architectures, if: (i) conservative controllers…

Optimization and Control · Mathematics 2018-03-06 Daniel O'Keeffe , Stefano Riverso , Laura Albiol-Tendillo , Gordon Lightbody

This work primarily focuses on synthesizing a controller that guarantees an unknown continuous-time system to be incrementally input-to-state stable ($\delta$-ISS). In this context, the notion of $\delta$-ISS control Lyapunov function…

Systems and Control · Electrical Eng. & Systems 2025-12-23 Ahan Basu , Bhabani Shankar Dey , Pushpak Jagtap

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