On the Function Space Controllability of Linear Neutral Systems

A criterion is derived for approximate controllability of linear autonomous neutral functional differential equations in the Sobolev space W₂⁽¹⁾ [ - h,0:Eⁿ ]. Controllability conditions are based on an abstract evolution equation representation of the system. An abstract criterion applicable to a general class of neutral systems is obtained and for the special case of matrix systems of the form \[{d}{{dt}}( {x(t) - A_1 x(t - h)} ) = E_0 x(t) + E_1 x(t - h) + Bu(t)\] this abstract criterion leads to an algebraic criterion.