Nonlinear Feedback Control Systems An Operator Theory Approach Rui J.P. de Figueiredo (Univ of California at Irvine) Guanrong Chen (Univ of Houston, Texas) Publisher: Academic Press, 1993, ISBN 0-12-208630-9, $64.95 Table of Contents --- Preface 1. Nonlinear Analytic Mappings 1.1. n-Linear Operators 1.2. Bounded n-Linear Operators 1.3. Normed Linear Spaces of Bounded n-Linear Operators 1.4. Continuous n-Linear Operators 1.5. Differentiation of Nonlinear Operators 1.6. Higher Order Derivatives of Nonlinear Operators 1.7. Infinite Power Series 1.8. Nonlinear Analytic Mappings 1.9. Nonlinear Volterra Mappings Exercises References 2. Nonlinear Lipschitz Operators 2.1. Preliminaries 2.2. Lipschitz Operators 2.3. Contraction Mapping Theorem 2.4. Generalized Lipschitz Operators 2.5. Differentiable Mappings Exercises References 3. Nonlinear Feedback Systems 3.1. Causality of Feedback Systems 3.2. The Small Gain Theorem 3.3. Stabilities of Control Systems 3.4. Stabilizing Nonlinear Feedbacks 3.5. Relationship Between Input-Output and Lyapunov Stabilities Exercises References 4. Optimal Design of Nonlinear Feedback Control Systems 4.1. Motivation for Optimal Feedback Controller Design 4.2. Optimal Tracking 4.3. Optimal Disturbance Rejection 4.4. Robust Stabilization Exercises References 5. Coprime Factorizations of Nonlinear Mappings for Control Systems 5.1. Preliminaries 5.2. Right Coprime Factorization of Nonlinear Feedback Systems 5.3. Necessary and Sufficient Condition and Construction of Coprime Factorizations 5.4. An Illustrative Example 5.5. Left Coprime Factorization for a Class of Nonlinear Control Systems 5.6. More on the Left Coprime Factorization Exercises References 6. Nonlinear System Identification 6.1. Problem Formulation 6.2. Lower and Upper Bounds 6.3. Existence of Optimal Algorithms 6.4. The Generalized Fock Space 6.5. Nonlinear System Identification Algorithms 6.6. Extension to Continuous-Time-Parameter Systems Exercises References Subject Index