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Related papers: Generalized definitions of discrete stability

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In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded finite rank perturbations. As the main result we characterize classes of perturbations preserving the strong stability of the…

Functional Analysis · Mathematics 2015-06-24 Lassi Paunonen

In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying…

Statistics Theory · Mathematics 2018-03-09 Thibaut Le Gouic , Quentin Paris

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…

Exactly Solvable and Integrable Systems · Physics 2014-08-27 V. E. Adler , V. V. Postnikov

The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…

Dynamical Systems · Mathematics 2022-10-25 Gheorghe Ivan

Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the…

Systems and Control · Computer Science 2018-07-30 Alexis J. Vallarella , Hernan Haimovich

This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square…

Optimization and Control · Mathematics 2024-06-25 Yuhao Tong , Steven W. Su

Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…

Methodology · Statistics 2025-06-04 Mahdi Nouraie , Samuel Muller

We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…

Classical Analysis and ODEs · Mathematics 2012-11-07 Eugene Polulyakh , Vladimir Sharko , Igor Vlasenko

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

In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis , Pierdomenico Pepe , Zhong-Ping Jiang

We survey stability properties of several families of moduli spaces, with a focus on braid groups and configuration spaces.

Algebraic Topology · Mathematics 2022-02-02 Rita Jimenez Rolland , Jennifer C. H. Wilson

We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…

Symbolic Computation · Computer Science 2017-05-09 Amir Hashemi , Michael Schweinfurter , Werner M. Seiler

A strong negative dependence property for measures on {0,1}^n - stability - was recently developed in [5], by considering the zero set of the probability generating function. We extend this property to the more general setting of…

Probability · Mathematics 2011-04-27 Thomas M. Liggett , Alexander Vandenberg-Rodes

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…

Data Analysis, Statistics and Probability · Physics 2012-10-05 Paolo Rossi

This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…

Optimization and Control · Mathematics 2020-09-08 Pieter Appeltans , Silviu-Iulian Niculescu , Wim Michiels

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

Optimization and Control · Mathematics 2018-11-06 Duc N. Tran , Björn S. Rüffer , Christopher M. Kellett

This paper is concerned with the problem of robust stabilization for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type, where the switching instants of the controller experience…

Dynamical Systems · Mathematics 2012-07-10 Shipei Huang , Zhengrong Xiang

Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the…

Numerical Analysis · Mathematics 2022-06-01 Tilman Alemán , Martin Halla , Christoph Lehrenfeld , Paul Stocker

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

Analysis of PDEs · Mathematics 2017-09-15 Nicolas Seguin

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

Dynamical Systems · Mathematics 2008-03-27 M. De la Sen