Fixed points and controllability in delay systems
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)=λ[G...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-02-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA/2006/41480 |
| Summary: | 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)=λ[G(t,xt)+(Bu)(t)],0<λ<1, then there exists a solution for λ=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. |
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| ISSN: | 1687-1820 1687-1812 |