Autor: Gil', Michael - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Input-to-state stability of neutral type systems
Autorzy:: Gil', Michael
Powiązania:: https://bibliotekanauki.pl/articles/729296.pdf
Data publikacji:: 2013
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: neutral type systems
causal mappings
input-to-state stability
Opis:: We consider the system
$ẋ(t) - ∫₀^{η} dR̃(τ) ẋ(t-τ) = ∫_0^{η} dR(τ)x(t-τ) + [Fx](t) + u(t)$
(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 systems, and the Ostrowski inequality for determinants.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 1; 5-16
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Spectrum localization of a perturbed operator in a strip and applications
Autorzy:: Gil', Michael
Powiązania:: https://bibliotekanauki.pl/articles/2051904.pdf
Data publikacji:: 2021
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: operator
spectrum
perturbation
approximation
integral operator
matrix
Opis:: Let $A$ and $\tilde{A}$ be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of $A$ lie in some strip. In what strip the spectrum of $\tilde{A}$ lies if $A$ and $\tilde{A}$ are “close”? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.
Źródło:: Opuscula Mathematica; 2021, 41, 3; 395-412
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components
Autorzy:: Gil’, Michael
Powiązania:: https://bibliotekanauki.pl/articles/29519485.pdf
Data publikacji:: 2024
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Hilbert space
linear operators
eigenvalues
Opis:: Let $ A $ be a bounded linear operator in a complex separable Hilbert space, $ A^∗ $ be its adjoint one and $ A_I := (A − A^∗)//(2i) $. Assuming that $A_I $ is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the eigenvalues of $ A $. Our results are formulated in terms of the “extended” eigenvalue sets in the sense introduced by T. Kato. Besides, we refine the classical Weyl inequality $ \Sigma_{k=1}^\infty (Im \lambda_k (A))^2 ≤ N_2^2 (A_I) $, where $ λk(A) (k = 1, 2, . . .) $ are the eigenvalues of $ A $ and $ N_2(·) $ is the Hilbert-Schmidt norm. In addition, we discuss applications of our results to the Jacobi operators.
Źródło:: Opuscula Mathematica; 2024, 44, 2; 241-248
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space
Autorzy:: Gil’, Michael
Powiązania:: https://bibliotekanauki.pl/articles/747089.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:: Abstract differential operator
spectrum
resolvent, stability
instability
Opis:: We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
Źródło:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2012, 66, 1
0365-1029
2083-7402
Pojawia się w:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Autorzy:: Gil', Michael
Powiązania:: https://bibliotekanauki.pl/articles/729497.pdf
Data publikacji:: 2014
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: matrix equations
norm estimates
perturbations
invariant subspaces
Opis:: Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 191-206
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: Exponential stability of nonlinear non-autonomous multivariable systems
Autorzy:: Gil', Michael
Powiązania:: https://bibliotekanauki.pl/articles/729507.pdf
Data publikacji:: 2015
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: nonlinear nonautonomous systems
exponential stability
absolute stability
Opis:: We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady state. As a particular case we obtain absolute stability conditions.
Our approach is based on a combined usage of the properties of the "frozen" Lyapunov equation, and recent norm estimates for matrix functions. An illustrative example is given.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 89-100
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

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