Coprime Factorization over a Class of Nonlinear Systems

Abstract

In this paper, we consider the problem of generalizing elements of linear coprime factorization theory to nonlinear systems characterized in terms of (possibly time varying) state dependent matrices A(x), B(x), C(x), D(x) and an initial state x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> . We achieve first right coprime factorizations for idealized situations. To achieve stable left factorizations we work with systems augmented by a direct feedthrough term where the input is reconstructible from the output. For nonlinear feedback control systems with plant and controller having stable left factorizations, then under appropriate regularity-conditions, earlier results have allowed the generation of the class of stabilizing controllers for a system in terms of an arbitrary stable system (parameter). Plant uncertainties, including unknown initial conditions, are modelled by means of a Yula-Kucera type parametrization approach developed for nonlinear systems. Certain robust stabilization results are also shown, and simulations demonstrate the regulation of nonlinear plants using the techniques developed. All the results are presented in such a way that specialization for the case of linear systems is immediate.