Controllability radii of linear neutral systems under structured perturbations

In this paper, we shall deal with the problem of calculation of the controllability radii of linear neutral systems of the form. <(x) over dot>(t) = A(0)x(t) + A(1)x(t - h) + A(-1)<(x) over dot>(t - h) + Bu(t). We will derive the definition of exact controllability radius, approximate controllability radius and Euclidean controllability radius for this system. By using multi-valued linear operators, the computable formulas for these controllability radii are established in the case where the system's coefficient matrices are subjected to structured perturbations. Some examples are provided to illustrate the obtained results.