A bang-bang theorem with bounds on the number of switchings

For systems of the form x = f(x)+ug(x), with f and g analytic, and -1 ?? u ?? 1, we state a bang-bang theorem with a priori bounds on the number of switchings, provided that the following condition is satisfied: in a neighborhood of every point x, it is possible to express, for each j, the vector field [g, (ad f)j (g)] as a linear combination of the (ad f)i (g), i ?? j+1, in such a way that the coefficient of (ad f)j+1 (g) in this expression is bounded in absolute value by a constant c < 1.