Abstract
The purpose of this paper is the approximate controllability of a counled mathematical system which provides a good model for important families of linear time invariant hereditary systems : delay differential equations, integro-differential equations, functional differential equations of retarded and neutral types etc. Necessary and sufficient conditions for approximate controllability are obtained, generalizing thus, the results of Manituis (1981), Bartosiewiez (1984), and Salamon (1984). The main results are expressed in an operator form, these are translated into conditions expressed in terms of the original system matrices. The approach used here is that of state SDace theory combined with an algebraic approach to functional differential equations.
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