Robust H∞ control of uncertain nonlinear systems

This paper discusses the robust L-2-gain performance synthesis problem for a class of uncertain nonlinear systems. It is shown that the Hamilton-Jacobi equation approach to robust H-infinity 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 L-2 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 L-2-gain performance of the closed-loop system are derived. Finally an example is given. (C) 2006 Elsevier Ltd. All rights reserved.