This book uses H∞ control methods to study robust state estimation and Lagrange stabilization of sector bounded nonlinear systems. Part A developed a new approach for constructing a robust state estimator for uncertain stochastic systems with slope-bounded nonlinearities satisfying IQC and multipliers are used to exploit the uncertainties and nonlinearities. Part B studies stability analysis and Lagrange stabilization of pendulum-like systems. This part proposes two Lagrange stability criteria which can be applied to more general pendulum-like systems. These results, with a sufficient condition for pendulum-likeness, enable Lagrange stabilization of pendulum-like systems with multiple nonlinearities to be formulated and solved in term of the solutions to game-type Riccati equations. This book generalizes some results in standard H∞ control. An extended strict bounded real lemma and a pseudo H∞ control theory are developed. The latter includes a pseudo strict bounded real lemma which relates a pseudo H∞ condition to the existence of a sign indefinite solution to a ARE. These results can handle some control design problems which the standard H∞ control theory is not applicable.