Non-robustness of continuous homogeneous stabilizers for affine control systems

A simple definition of robustness of asymptotic stabilizers with respect to modeling errors is adopted. Two theorems giving sufficient conditions for the non-robustness of continuous homogeneous ρ-exponential stabilizers are then stated; the first one applies to systems that may contain a drift term, while the second one concerns driftless systems. One of the consequences of these results is that for chained form systems, no continuous homogeneous ρ-exponential stabilizer (several of which exist in the literature) can be robust in the sense defined herein. Two examples illustrate applications of these results