International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 29 |Article ID 419587 | 12 pages | https://doi.org/10.1155/S0161171202010840

On the Lyapunov equation in Banach spaces and applications to control problems

Received30 Aug 2000
Revised05 Mar 2001

Abstract

By extending the Lyapunov equation A*Q+QA=P to an arbitrary infinite-dimensional Banach space, we give stability conditions for a class of linear differential systems. Relationship between stabilizability and exact null-controllability is established. The result is applied to obtain new sufficient conditions for the stabilizability of a class of nonlinear control systems in Banach spaces.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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