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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2006-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2006/41480 |
| Summary: | <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> |
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| ISSN: | 1687-1820 1687-1812 |