Abstract
An adaptive algorithm is constructed for controlling an unstable first order differential equation having a time-varying input delay. A version of a finite spectrum assignment control law applicable to time-varying delays is developed and applied as the adaptive law. The control objective is to get the closed-loop system to follow asymptotically a given stable input delat model. The parameter adjustment law is a typical modek reference law obtained via a quadratic Lyapunov function. The adaptive control algorithym is proved to be globally stabilizing and to result in output convergence.
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