Initial data stability and admissibility of spaces for Itô linear difference equations

Ramazan Kadiev; Pyotr Simonov

Displaying similar documents to “Initial data stability and admissibility of spaces for Itô linear difference equations”

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...

Stability analysis of phase boundary motion by surface diffusion with triple junction

Harald Garcke, Kazuo Ito, Yoshihito Kohsaka (2009)

Banach Center Publications

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The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the $H^{- 1}$ -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.

Input-to-state stability of neutral type systems

Michael I. Gil' (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider the system $ẋ (t) - \int ₀^{η} d R ̃ (τ) ẋ (t - τ) = \int_{0}^{η} d R (τ) x (t - τ) + [F x] (t) + u (t)$ (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered...

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 $t \to \infty$ .

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. ...

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.

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.

On stability of linear neutral differential equations with variable delays

Leonid Berezansky, Elena Braverman (2019)

Czechoslovak Mathematical Journal

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We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $\dot{x} (t) - a (t) \dot{x} (g (t)) + b (t) x (h (t)) = 0,$ where $| a (t) | < 1, b (t) \geq 0, h (t) \leq t, g (t) \leq t,$ and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

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 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...

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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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.