Riccati equation approach to robust L 2-gain synthesis for a class of uncertain nonlinear systems

This paper discusses the robust L 2-gain performance synthesis problem for a class of nonlinear uncertain systems. It is shown that the Riccati equation approach to H ∞ robust performance synthesis can be extended to solve this problem. Based on a positive definite solution of a Riccati inequality, a sufficient condition is given such that the nonlinear uncertain system is robust stable and its L 2 gain is less than one. Using this condition, a state feedback law which ensures robust L 2-gain performance of the closed-loop system is derived. The state feedback law is equivalent to the solution of an H ∞ standard design problem for an extended plant parametrized by scaling parameters. Finally, a design example and simulation results are given.