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Fixed points and controllability in delay systems


Schaefer's fixed point theorem is used to study the controllability in an infinite delay system . 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 , then there exists a solution for . 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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Correspondence to Bo Zhang.

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Gao, H., Zhang, B. Fixed points and controllability in delay systems. Fixed Point Theory Appl 2006, 41480 (2006).

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