- Tytuł:
- The motion planning problem and exponential stabilization of a heavy chain. Part II
- Autorzy:
- Grabowski, P.
- Powiązania:
- https://bibliotekanauki.pl/articles/255394.pdf
- Data publikacji:
- 2008
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
infinite-dimensional control systems
semigroups
motion planning problem
exponential stabilization
spectral methods
Riesz bases
exact observability - Opis:
- 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.
- Źródło:
-
Opuscula Mathematica; 2008, 28, 4; 481-505
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł