Controllability and Tenability of Nonlinear Systems with State Equality Constraints

In this paper we consider the problem of maintaining a state equality constraint throughout an interval $[a,c]$ in spite of small perturbations of the dynamic and constraint equations. We obtain sufficient conditions for this to be possible in terms of the behavior of the associated linear variational systems. These results extend similar conditions for the local controllability of nonlinear systems obtained by Markus [2] and Yorke [7].