The linear stabilization problem in Hilbert space

Slemrod, Marshall

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Publication date

November 1972

DOI

10.1016/0022-1236(72)90073-0

Publisher

Published by Elsevier Inc.

Abstract

AbstractWe consider the linear control system ẋ = Ax + Bu. Here A is the infinitesmal generator of a strongly continuous group of bounded linear operators T(t) on a Hilbert space E, B is a bounded linear operator from a Hilbert space H to E. We give sufficient conditions for the existence of a bounded linear operator K from E to H so that the control system with feedback control law u(t) = Kx(t) has the zero solution asymptotically stable. The results reduce to a well-known theorem of Kalman in the case E, H are finite dimensional