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...
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| Format: | Article |
| Language: | English |
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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 |
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doaj-be7be39918874374864f04ad59d8bb552020-11-25T00:23:34ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-02-01200610.1155/FPTA/2006/41480Fixed points and controllability in delay systemsBo ZhangHang GaoSchaefer'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.http://dx.doi.org/10.1155/FPTA/2006/41480 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bo Zhang Hang Gao |
| spellingShingle |
Bo Zhang Hang Gao Fixed points and controllability in delay systems Fixed Point Theory and Applications |
| author_facet |
Bo Zhang Hang Gao |
| author_sort |
Bo Zhang |
| title |
Fixed points and controllability in delay systems |
| title_short |
Fixed points and controllability in delay systems |
| title_full |
Fixed points and controllability in delay systems |
| title_fullStr |
Fixed points and controllability in delay systems |
| title_full_unstemmed |
Fixed points and controllability in delay systems |
| title_sort |
fixed points and controllability in delay systems |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2006-02-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/FPTA/2006/41480 |
| work_keys_str_mv |
AT bozhang fixedpointsandcontrollabilityindelaysystems AT hanggao fixedpointsandcontrollabilityindelaysystems |
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1716178726954205184 |