Consistent Discretization of Homogeneous Models

Abstract

A discretization of continuous-time models is an important issue for the digital implementation of homogeneous control algorithms as well as for the numerical simulation of homogeneous controlled processes. This is a nontrivial task even in the finite-dimensional space. The explicit Euler discretization of a stable homogeneous system with nonzero degree is never globally asymptotically stable, but the implicit Euler discretization (being stable) does not preserve a convergence rate of the original continuous-time system. In other words, the classical discretization schemes are not appropriate for homogeneous models. This chapter introduces a new methodology of a consistent discretization, which allows all important properties of the continuous-time homogeneous system to be preserved in its discrete-time counterpart. The developed scheme is shown to be useful for the discretization of the homogeneous control algorithm designed in Chap. 9.