International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 155-166
doi:10.1155/S0161171202010840
On the Lyapunov equation in Banach spaces and applications to control problems
Vu Ngoc Phat1
and Tran Tin Kiet2
1Institute of Mathematics, Box 631, Bo Ho, Hanoi 10.000, Vietnam
2Department of Mathematics, Quinhon Pedagogical University, Binh Dinh, Qui Nhon City, Vietnam
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.