Accession Number:
ADA043852
Title:
A Note on Weak Stabilizability of Contraction Semigroups,
Descriptive Note:
Corporate Author:
CALIFORNIA UNIV LOS ANGELES DEPT OF SYSTEM SCIENCE
Personal Author(s):
Report Date:
1977-07-01
Pagination or Media Count:
17.0
Abstract:
A recent result on weak stabilizability is that the system x sub n Ax Bu, where A is the infinitesimal generator of a contraction semigroup over a Hilbert Space H, and B is linear bounded is weakly stabilizable if i A has a compact resolvent and ii A,B is approximately controllable. In this note, we show that condition i is superfluous and ii can be weakened to iii the weakly unstable states are approximately controllable, which actually turns out to be a necessary condition. Indeed, if i is verified, iii is necessary and sufficient for strong stabilizability. Moreover, a simple, direct proof is given using semigroup theoretic techniques.
Descriptors:
Subject Categories:
- Theoretical Mathematics