This paper presents a unified and extended approach to L2-gain analysis of smooth nonlinear systems using invariant manifolds and inequalities, and their relation to Hamiltonian vector fields. The author extends the state-space approach to linear H∞ control to a nonlinear analog, focusing on the state feedback H∞ optimal control problem. The paper also explores the relationship between the L2-gain of a nonlinear system and the L2-gain (or H∞ norm) of its linearized system. Key results include the existence of a smooth solution to the Hamilton-Jacobi equation or inequality, which implies the L2-gain property for the nonlinear system. Additionally, the paper discusses the stability of the closed-loop system and provides conditions for the existence of a smooth solution to the Hamilton-Jacobi equation. The paper concludes with an analog of linear H∞ control theory for nonlinear systems, including the linearization of the Hamiltonian vector field and the conditions for the existence of a smooth solution to the Hamilton-Jacobi equation.This paper presents a unified and extended approach to L2-gain analysis of smooth nonlinear systems using invariant manifolds and inequalities, and their relation to Hamiltonian vector fields. The author extends the state-space approach to linear H∞ control to a nonlinear analog, focusing on the state feedback H∞ optimal control problem. The paper also explores the relationship between the L2-gain of a nonlinear system and the L2-gain (or H∞ norm) of its linearized system. Key results include the existence of a smooth solution to the Hamilton-Jacobi equation or inequality, which implies the L2-gain property for the nonlinear system. Additionally, the paper discusses the stability of the closed-loop system and provides conditions for the existence of a smooth solution to the Hamilton-Jacobi equation. The paper concludes with an analog of linear H∞ control theory for nonlinear systems, including the linearization of the Hamiltonian vector field and the conditions for the existence of a smooth solution to the Hamilton-Jacobi equation.