Controllability and strong controllability of differential inclusions

In this paper, we prove sufficient conditions for controllability and strong controllability in terms of the Mordukhovich subdifferential for two classes of differential inclusions. The first one is the class of sub-Lipschitz multivalued functions introduced by Loewen–Rockafellar (1994) [10]. The second one, introduced recently by Clarke (2005) [18], is the class of multivalued functions which are pseudo-Lipschitz and satisfy the so-called tempered growth condition. To do this, we establish an error bound result in terms of the Mordukhovich subdifferential outside Asplund spaces.