Input-to-state stability of neutral type systems

Michael I. Gil'

Displaying similar documents to “Input-to-state stability of neutral type systems”

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

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This paper is devoted to the investigation on the stability for two characteristic functions $f_{1} (z) = z^{2} + p e^{- z τ} + q$ and $f_{2} (z) = z^{2} + p z e^{- z τ} + q$ , where $p$ and $q$ are real numbers and $τ > 0$ . The obtained theorems describe the explicit stability dependence on the changing delay $τ$ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Practical $h$ -stability behavior of time-varying nonlinear systems

Abir Kicha, Hanen Damak, Mohamed Ali Hammami (2023)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the problem of practical uniform $h$ -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform $h$ -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results. ...

On approximation of stability radius for an infinite-dimensional feedback control system

Hideki Sano (2016)

Kybernetika

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In this paper, we discuss the problem of approximating stability radius appearing in the design procedure of finite-dimensional stabilizing controllers for an infinite-dimensional dynamical system. The calculation of stability radius needs the value of $H_{\infty}$ -norm of a transfer function whose realization is described by infinite-dimensional operators in a Hilbert space. From the computational point of view, we need to prepare a family of approximate finite-dimensional operators and then to...

Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan

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Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level $n + 0.5$ (i.e., mean values of old and new time step) to $n + 1$ (i.e., only from new time step). Stable solution was obtained only...

Steady state in a biological system: global asymptotic stability

Maria Adelaide Sneider (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron $K$ , is globally asymptotically stable in $K$ . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.

Steady state in a biological system: global asymptotic stability

Maria Adelaide Sneider (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Stability of nonlinear $h$ -difference systems with $n$ fractional orders

Małgorzata Wyrwas, Ewa Pawluszewicz, Ewa Girejko (2015)

Kybernetika

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In the paper we study the subject of stability of systems with $h$ -differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with $n$ fractional orders. The equivalent descriptions of fractional $h$ -difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with $n$ -orders.

The central heights of stability groups of series in vector spaces

Bertram A. F. Wehrfritz (2016)

Czechoslovak Mathematical Journal

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We compute the central heights of the full stability groups $S$ of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such $S$ proved recently by Casolo & Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for...

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

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We consider the equation $x^{''} + a^{2} (t) x = 0, a (t) : = a_{k} if t_{k - 1} \leq t < t_{k}, for k = 1, 2, ...,$ where ${a_{k}}$ is a given increasing sequence of positive numbers, and ${t_{k}}$ is chosen at random so that ${t_{k} - t_{k - 1}}$ are totally independent random variables uniformly distributed on interval $[0, 1]$ . We determine the probability of the event that all solutions of the equation tend to zero as $t \to \infty$ .

Quantitative stability for sumsets in $ℝ^{n}$

Alessio Figalli, David Jerison (2015)

Journal of the European Mathematical Society

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Given a measurable set $A \subset ℝ^{n}$ of positive measure, it is not difficult to show that $| A + A | = | 2 A |$ if and only if $A$ is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If $(| A + A | - | 2 A |) / | A |$ is small, is $A$ close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between $A$ and its convex hull in terms of $(| A + A | - | 2 A |) / | A |$ .

Addition theorems and related geometric problems of group representation theory

Ekaterina Shulman (2013)

Banach Center Publications

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The Levi-Civita functional equation $f (g h) = \sum_{k = 1}^{n} u_{k} (g) v_{k} (h)$ (g,h ∈ G), for scalar functions on a topological semigroup G, has as the solutions the functions which have finite-dimensional orbits in the right regular representation of G, that is the matrix elements of G. In considerations of some extensions of the L-C equation one encounters with other geometric problems, for example: 1) which vectors x of the space X of a representation $g \mapsto T_{g}$ have orbits O(x) that are “close” to a fixed finite-dimensional subspace?...

Asymptotic stability of a system of randomly connected transformations on Polish spaces

Katarzyna Horbacz (2001)

Annales Polonici Mathematici

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We give sufficient conditions for the existence of a matrix of probabilities ${[p_{i k}]}_{i, k = 1}^{N}$ such that a system of randomly chosen transformations $Π_{k}$ , k = 1,...,N, with probabilities $p_{i k}$ is asymptotically stable.