  In this article we study control problems with systems that are governed by
ordinary differential equations whose vector fields depend linearly in the time
derivatives of some components of the control. The remaining components are
considered as classical controls. This kind of system is called `impulsive
system'. We assume that the vector fields multiplying the derivatives of each
component of the control are commutative. We derive new necessary conditions in
terms of the adjoint state and the Lie brackets of the data functions.
