Robustness of stability of linear state space systems with respect to time-varying, nonlinear and dynamic perturbations

The role that perturbations of the static linear output feedback type play in robustness analysis is discussed. It is noted that the class of these perturbations does not even contain all the time-invariant affine perturbations of the system matrix, and that it is questionable what the robustness measures r_R and r_C, which are the real and complex stability radii, mean in the presence of time-varying, nonlinear or dynamic perturbations of the system equation. Since r_R and r_C are relative to a very restricted class of perturbations, it is suspected that they are misleading, i.e., overoptimistic indicesof robustness. The authors investigate this, and show that in the presence of uncertainty about the class of perturbations the real stability radius r_R may overestimate the robustness of the system