Fixed points and controllability in delay systems
<p/> <p>Schaefer's fixed point theorem is used to study the controllability in an infinite delay system <inline-formula><graphic file="1687-1812-2006-41480-i1.gif"/></inline-formula>. A compact map or homotopy is constructed enabling us to show that if th...
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2006-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2006/41480 |
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doaj-f7f98fea58bf42978652641d48b6602f2020-11-25T01:08:07ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-01-012006141480Fixed points and controllability in delay systemsZhang BoGao Hang<p/> <p>Schaefer's fixed point theorem is used to study the controllability in an infinite delay system <inline-formula><graphic file="1687-1812-2006-41480-i1.gif"/></inline-formula>. A compact map or homotopy is constructed enabling us to show that if there is an <it>a priori</it> bound on all possible solutions of the companion control system <inline-formula><graphic file="1687-1812-2006-41480-i2.gif"/></inline-formula>, then there exists a solution for <inline-formula><graphic file="1687-1812-2006-41480-i3.gif"/></inline-formula>. The <it>a priori</it> 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.</p> http://www.fixedpointtheoryandapplications.com/content/2006/41480 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhang Bo Gao Hang |
| spellingShingle |
Zhang Bo Gao Hang Fixed points and controllability in delay systems Fixed Point Theory and Applications |
| author_facet |
Zhang Bo Gao Hang |
| author_sort |
Zhang Bo |
| 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 |
2006-01-01 |
| description |
<p/> <p>Schaefer's fixed point theorem is used to study the controllability in an infinite delay system <inline-formula><graphic file="1687-1812-2006-41480-i1.gif"/></inline-formula>. A compact map or homotopy is constructed enabling us to show that if there is an <it>a priori</it> bound on all possible solutions of the companion control system <inline-formula><graphic file="1687-1812-2006-41480-i2.gif"/></inline-formula>, then there exists a solution for <inline-formula><graphic file="1687-1812-2006-41480-i3.gif"/></inline-formula>. The <it>a priori</it> 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.</p> |
| url |
http://www.fixedpointtheoryandapplications.com/content/2006/41480 |
| work_keys_str_mv |
AT zhangbo fixedpointsandcontrollabilityindelaysystems AT gaohang fixedpointsandcontrollabilityindelaysystems |
| _version_ |
1715847888736616448 |