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.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE