The proofs of Lemma 5.2 and Theorem 5.1 in [SIAM J. Control Optim., 38 (2000), pp. 947-970] have a common error which concerns the existence of (locally) Lipschitz selections. Indeed, Lemma 5.2 is true in the case where the multivalued mapping G is convex-valued, and in our case this assumption is not satisfied. So some modifications are needed. The statement of Theorem 5.1 (which does not use Lemma 5.2) is as follows.