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”

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

Harald Garcke, Kazuo Ito, Yoshihito Kohsaka (2009)

Banach Center Publications

Similarity:

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

Similarity:

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

Similarity:

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 $t \to \infty$ .

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

Małgorzata Wyrwas, Ewa Pawluszewicz, Ewa Girejko (2015)

Kybernetika

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

On the stability of the functional equation of the first order

Erwin Turdza (1970)

Annales Polonici Mathematici

Similarity:

On the inverse stability of functional equations

Zenon Moszner (2013)

Banach Center Publications

Similarity:

The inverse stability of functional equations is considered, i.e. when the function, approximating a solution of the equation, is an approximate solution of this equation.

On the Normal Stability of Functional Equations

Zenon Moszner (2016)

Annales Mathematicae Silesianae

Similarity:

In the paper two types of stability and of b-stability of functional equations are distinguished.

$\aleph_{1}$ -Boolean spectrum, and stability

Piero Mangani, Annalisa Marcja (1982)

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

Similarity:

Si dimostra che la conoscenza delle algebre di Boole dei definibili di modelli di cardinità $\aleph_{1}$ di una teoria elementare è sufficiente per decidere il suo tipo di stabilità.

Boundedness and stability in nonlinear delay difference equations employing fixed point theory.

Islam, Muhammad, Yankson, Ernest (2005)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Similarity:

Stability in linear neutral difference equations with variable delays

Abdelouaheb Ardjouni, Ahcene Djoudi (2013)

Mathematica Bohemica

Similarity:

In this paper we use the fixed point method to prove asymptotic stability results of the zero solution of a generalized linear neutral difference equation with variable delays. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Y. N. Raffoul (2006), E. Yankson (2009), M. Islam and E. Yankson (2005).