L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / 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. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H/sub infinity / control, namely the state feedback H/sub infinity / optimal control problem. Furthermore, the relation with H/sub infinity / control of the linearized system is dealt with.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>