A Note on Weak Stabilizability of Contraction Semigroups,

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1977
Accession Number
ADA043852

Entities

People

  • Claude D. Benchimol

Organizations

  • University of California, Los Angeles

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  • Counter IED

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  • Mathematics

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  • Control Systems Engineering.
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