Szczegóły publikacji
Opis bibliograficzny
Small-gain theorem for a class of abstract parabolic systems / Piotr GRABOWSKI // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2018 — vol. 38 no. 5, s. 651–680. — Bibliogr. s. 679, Abstr. — Wyniki zawarte w artykule zostały przedstawione na konferencji: Spectral Theory and Applications (STA2017) : May 30–June 3, 2017, Kraków, Poland
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 115497 |
|---|---|
| Data dodania do BaDAP | 2018-07-27 |
| Tekst źródłowy | URL |
| DOI | 10.7494/OpMath.2018.38.5.651 |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Opuscula Mathematica : rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica |
Abstract
We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be described by unbounded operators. It is assumed that the observation operator is admissible but the control operator may be not. Such a system is controlled in a feedback loop by a controller with static characteristic being a globally Lipschitz map from the space of outputs into the space of controls. Our main interest is to obtain a perturbation theorem of the small-gain-type which guarantees that null equilibrium of the closed-loop system will be globally asymptotically stable in Lyapunov's sense.
