Szczegóły publikacji
Opis bibliograficzny
The motion planning problem and exponential stabilization of a heavy chain, Pt. 2 / Piotr GRABOWSKI // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2008 — vol. 28 no. 4, s. 481–505. — Bibliogr. s. 503–504, Abstr.
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 43909 |
|---|---|
| Data dodania do BaDAP | 2009-02-21 |
| Tekst źródłowy | URL |
| Rok publikacji | 2008 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Opuscula Mathematica : rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica |
Abstract
This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
