The structured controllability radii of higher order systems

In this paper we shall deal with the problem of calculation of the controllability radius of higher order dynamical systems of the form Ex(k)(t)=Ak-1x(k-1)(t)+⋯+A1x(1)(t)+A0x(t)+Bu(t) where the leading coefficient matrix E need not assumed to be non-singular. By using multi-valued linear operators we are able to derive computable formulas of the controllability radius under the assumption that the system’s coefficient matrices are subjected to structured affine perturbations. Some examples are provided to illustrate the obtained results.