Autor: Gil', Michael - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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: 2.

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

Skocz do pozycji: 3.

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

Informacja