The structured controllability radius of linear delay systems

In this article, we shall deal with the problem of calculation of the controllability radius of a delay dynamical systems of the form x′(t) = A 0 x(t) + A 1 x(t − h 1) + ··· + A k x(t − h k ) + Bu(t). By using multi-valued linear operators, we are able to derive computable formulas for the controllability radius of a controllable delay system in the case where the system's coefficient matrices are subjected to structured perturbations. Some examples are provided to illustrate the obtained results.