A SUFFICIENT CONDITION FOR THE CONSISTENCY OF A PIECEWISE LINEAR APPROXIMATION OF A NOLINEAR AFFINE SYSTEM

For a controlled nonlinear affine system, a piecewise linear approximation in the form of a switched affine system is considered. The concept of consistency of a piecewise linear approximation is introduced when the system is closed by a variable structure controller. The consistency of the approximation ensures the equality of the graphs of discrete states 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 its fulfillment is proposed.