Radius of approximate controllability of linear retarded systems under structured perturbations

In this paper we shall deal with the problem of calculation of the radius of approximate controllability in the Banach state space Kn×L2([−hk,0],Kn)Kn×L2([−hk,0],Kn) for linear retarded systems of the form ẋ(t)=A0x(t)+A1x(t−h1)+⋯+Akx(t−hk)+Bu(t). By using multi-valued linear operators we are able to derive computable formulas for this radius when the system’s coefficient matrices are subjected to structured perturbations. Some examples are provided to illustrate the obtained results.