An L Disturbance Attenuation Solution to the Nonlinear Benchmark Problem

In this paper we use the theory of L disturbance attenuation for linear H and nonlinear systems to obtain solutions to the Nonlinear Benchmark Problem NLBP proposed in the paper by Bupp et al By considering a series expansion solution to the Hamilton Jacobi Isaacs Equation associated with the nonlinear disturbance attenuation problem we obtain a series expansion solution for a nonlinear controller Numerical simulations compare the performance of the third order approximation of the nonlinear controller with its rst order approximation which is the same as the linear H controller obtained from the linearized problem