Discretization of continuous controllable systems based on generalized solutions

Discretization of continuous processes is a typical procedure for the construction of computational algorithms. However, the simplest discretization methods based on piecewise constant control may turn out to be incorrect when the expected solution has the form of a sliding or impulse sliding mode. For correct and efficient discretization, we propose to use generalized solutions of continuous systems described in a regular way via relaxing extensions. We also propose an implicit scheme that uses the concept of a model for a discrete-continuous process. Examples are given.