On the Lyapunov equation in Banach spaces and applications to control problems-Reference-Cited by-同舟云学术

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

Published:2002 Issue:3 Volume:29 Page:155-166
ISSN:0161-1712
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Phat Vu Ngoc¹,Kiet Tran Tin²

Affiliation:

1. Institute of Mathematics, Box 631, Bo Ho, Hanoi 10.000, Vietnam

2. Department of Mathematics, Quinhon Pedagogical University, Binh Dinh, Qui Nhon City, Vietnam

Abstract

By extending the Lyapunov equationA*Q+QA=−Pto 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.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2002/419587.pdf

Cited by 19 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Boundary-Value Problems for the Lyapunov Equation. I;Ukrainian Mathematical Journal;2024-08

2. Крайові задачі для рівняння Ляпунова. І;Ukrains’kyi Matematychnyi Zhurnal;2024-03-25

3. BOUNDARY VALUE PROBLEMS FOR THE LYAPUNOV EQUATION;Journal of Numerical and Applied Mathematics;2023

4. Practical Exponential Stabilization for Semi-Linear Systems in Hilbert Spaces;State Estimation and Stabilization of Nonlinear Systems;2023

5. Stabilization of non-autonomous infinite-dimensional systems depending on a parameter;International Journal of Computer Mathematics;2022-11-22