A Note on Complete Controllability and Stabilizability for Linear Control Systems in Hilbert Space
Author:
- Marshall SlemrodMSMarshall Slemrod
- 1 August 1974
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control
- Vol. 12 (3) , 500-508
Abstract
We consider the linear control system $\dot x = Ax + Bu$. Here A is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators $T(t)$ on a Hilbert space E, and 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. In particular, we study the relationship between the concept of complete controllability and the existence of K.
Keywords
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