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Null controllability of a class of functional differential systems. (English) Zbl 0662.93008
The authors prove that spectral controllability implies null controllability for a class of functional differential equations. This assertion appears, as the authors mention, in earlier papers by Marchenko and by the reviewer who used results due to Watanabe. However this important paper presents the first clear and reliable proof, using algebraic methods. They show that null controllability is equivalent to the solvability of a certain matrix Bézout equation over appropriate subrings of the ring of entire functions. Then spectral controllability implies that this equation can be solved.
Reviewer: F.Colonius

MSC:
93B05 Controllability
34K35 Control problems for functional-differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B03 Attainable sets, reachability
93B25 Algebraic methods
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