Robust H∞ control of uncertain nonlinear systemvia state feedback

This technical note presents a solution of robust H_∞ control problem for an affine nonlinear system with gain bounded uncertainty. It is shown that the L₂-induced norm of a closed-loop system with the uncertainty is less than one if an extended nonlinear system with no uncertainty is dissipative with respect to a supply rate. In consequence of this result, a state feedback law such that the closed-loop system has H_∞ robust performance is derived based on the Hamilton-Jacobi inequality. It is also shown that the existing results for linear systems are special cases of the presented results