Fixed points and controllability in delay systems
Document Type
Article
Publication Date
3-29-2006
Abstract
Schaefer's fixed point theorem is used to study the controllability in an infinite delay system x? (t) = G(t,xt) + (Bu)(t). A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system x? (t) = ?[G(t,xt) + (Bu)(t)], 0 < ? < 1, then there exists a solution for ? = 1. The a priori bound is established by means of a Liapunov functional or applying an integral inequality. Applications to integral control systems are given to illustrate the approach. Copyright © 2006 H. Gao and B. Zhang.
Recommended Citation
Gao, Hang and Zhang, Bo, "Fixed points and controllability in delay systems" (2006). College of Health, Science, and Technology. 1039.
https://digitalcommons.uncfsu.edu/college_health_science_technology/1039