Abstract
In this paper, we study the problem of stabilizing one-dimensional parabolic systems with input delay. Especially, we consider the case of “distributed control”. The purpose is to derive the stabilizing controller of predictor type in an abstract space, by using a backstepping method combined with the semigroup theory. The use of the semigroup theory makes the proof of continuity of the inverse transformation easy. Also, it is shown that the abstract controller can be actually implemented by using a finite number of eigenvalues and eigenfunctions of the system operator. Finally, a numerical simulation result is presented to demonstrate our design method.
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