Robust Stabilization of Nonlinear Systems via Normalized Coprime Factor Representations

Abstract

A reasonably complete theory for the synthesis of robust controllers for a broad class of nonlinear systems is now available. We use this theory to generalize the linear theory of normalized coprime factor robustness optimization to the case of affine input nonlinear systems. In particular, we show that the equilibrium controller may be characterized in terms of the stabilizing and destabilizing solutions of the Hamilton–Jacobi equation used to calculate the normalized (right) coprime factors of the plant. We also show that the optimal robustness margin of √ 1− M N 2 H generalizes to the nonlinear case. In preparation for the nonlinear analysis, we review the linear case in a way which motivates our approach to the nonlinear case and highlights the parallels with it.