Abstract
The problem of approximate controllability for general linear functional - differential systems of retarded type with instant trajectory values in Rn is considered. The function spaces C, wr1 and Mrαβ as a generalization of Lr = Mr00 are tried for state space. It occurs that so called multipoint or weak multipoint controllability is necessary for approximate controllability in suitable function space. The dual system obtained by matrix transposition is presented and observability problems, dual to approximate controllability, are described. They allow to derive simple checkable either necessary or sufficient conditions for basic problems, to characterize in which function space approximate controllability is the stronger property and to get an important result that approximate controllability in any of the spaces Wr1, C, Mr11 and Mr01 implies eigenvalue assignability with the aid of linear state feedback. Complete algebraic testable characterization of approximate controllability is derived for one delay case extendable to the case of finitely many commensurable delays. The full version of this paper with proofs is available as technical report [24].
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