We describe a method for the design of feedback stabilization control laws for nonlinear systems using the theory of normal forms and the results from optimal control theory. We show that the resulting controllers can provide a larger region of stability than local linear controllers designed to perform the same task.
Walker, D. M., Froyland, G., Judd, K., & Mees, A. I. (2003). Controllers for Nonlinear Systems Using Normal Forms. International Journal of Bifurcation and Chaos, 13(2), 459-465. https://doi.org/10.1142/S0218127403006637