Abstract
Necessary and sufficient conditions of approximate controllability, in the space $R^n \times L_2 ([ - h,0],R^n )$, of general linear retarded systems are obtained. It is shown that approximate controllability is equivalent to two conditions: a) spectral controllability, and b) the existence of linear feedback which transforms the original system into a system with a complete set of generalized eigenfunctions. Both conditions are expressed in algebraic form. The proof of this result is based on recently obtained criteria of completeness of generalized eigenfunctions associated with retarded systems and on an algebraic approach to functional differential equations. Practical verifiability of the new conditions is demonstrated on several examples.
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