International Journal of Control, Vol.64, No.6, 1177-1188, 1996
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-infinity 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-infinity standard design problem for an extended plant parametrized by scaling parameters. Finally, a design example and simulation results are given.