Robust H∞H∞ control of uncertain nonlinear systems

This paper discusses the robust L2L2-gain performance synthesis problem for a class of uncertain nonlinear systems. It is shown that the Hamilton–Jacobi equation approach to robust H∞H∞ performance synthesis can be extended to solve this problem. Based on a positive-definite solution of a Hamilton–Jacobi inequality, a sufficient condition is given such that the uncertain nonlinear system is robust and stable and its L2L2 gain is less than or equal to a prescribed value. Using this condition, a state feedback law and an output feedback law which ensure robust L2L2-gain performance of the closed-loop system are derived. Finally an example is given.