The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward H∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation.
van der Schaft, A. (1995). Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty. Systems and control letters, 24(24), 75-81. https://doi.org/10.1016/0167-6911(94)00038-W