Corrigendum to "Hierarchical trajectory refinement for a class of nonlinear systems" [Automatica 41(4) (2005) 701-708]

It was recently brought to our attention by Dr. Mario Sigalotti that Theorem 3.2 in Tabuada and Pappas (2005) does not hold under the stated assumptions. In particular, the following example presented by Dr. Mario Sigalotti contradicts Corollary 3.3. Let r = k = 1, X0 M(y, z)= arctan(z) / y, X1 M(y, z)= / z, (y, z)= y. It is easy to check that A.I, A.II, A.III, and (3.4) hold true. Using (2.3) we get FN(y, ( , , ))= . Therefore, every smooth trajectory y(·) inR should be a solution of N . If |ẏ(t)|> /2 for some t ∈ R, however, then y(·) cannot be refined to a trajectory of M . The problem lies in Lemma 3.1 which does not hold under the stated assumptions. However, it does hold under the stronger assumption [ker(T ), [ker(T ),AM ]] ⊆ ker(T ) (1)