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

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. © 2002 Hindawi Publishing Corporation. All rights reserved.