Sufficient Condition for the Consistency of a Piecewise LinearApproximation to a Nolinear Affine System

For a controlled nonlinear affine system, a piecewise linear approximation in the form of a switched affine system is considered. We introduce the concept of consistency of the piecewise linear approximation for the system closed by a variable structure controller. The consistency of the approximation ensures the equality of the discrete state graphs of the nonlinear system itself and its piecewise linear approximation. A sufficient condition for the consistency of the approximation is obtained, and an approach to numerical verification of this condition is proposed.