On controllability for a nonlinear differential inclusion

We consider a nonlinear differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory. To derive this result we use convex linearizations of the nonlinear differential inclusion. More precisely, we show that the nonlinear differential inclusion is h-locally controlable around a solution z if a certain linearized inclusion is lambda-locally controlable around the null solution for every lambda is an element of partial derivative h(z(T)), where partial derivative h denotes Clarke's generalized Jacobian of the locally Lipschitz function h.