Applying Continuous Piecewise Linear Approximations to Affine Non-Linear Control systems

In this paper continuous piecewise linear (CPWL) approximations of non-linear affine control systems are considered. An optimal control context allows to determine asymptotic error bounds between real and approximate control systems. Then it is possible to apply the controller designed using the CPWL approximation to the real vector field with guarantee of stability. An example is presented to show the potential applications of these ideas.