Approximate controllability of neutral systems with delays in control

In this paper we examine approximate controllability in the space IV: x L* of linear neutral systems with general delays in states and controls. We define spectral controllability and completability of such systems and prove that these properties together are equivalent to the approximate controllability in Wt x L*. We give necessary and sufficient conditions for the approximate controllability which extend recent results of Manitius [9] to neutral systems with delays in control. Let us consider a linear neutral control system described by the following functional-differential equation

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