Fixed Points and Controllability in Delay Systems
نویسندگان
چکیده
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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