L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control

Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. Based upon these results a nonlinear analog is obtained of the simplest part of the recently developed state-space approach to linear H∞ control, namely the state feedback H∞ optimal control problem. Furthermore, the relation with H∞ control of the linearized system is dealt with.