ContentsPreface xi1. Introduction 11.1 Why Nonlinear Control ? 11.2 Nonlinear System Behavior 41.3 An Overview of the Book 121.4 Notes and References 13Part I: Nonlinear Systems Analysis 14Introduction to Part I 142. Phase Plane Analysis 172.1 Concepts of Phase Plane Analysis 182.1.1 Phase Portraits 182.1.2 Singular Points 202.1.3 Symmetry in Phase Plane Portraits 222.2 Constructing Phase Portraits 232.3 Determining Time from Phase Portraits 292.4 Phase Plane Analysis of Linear Systems 302.5 Phase Plane Analysis of Nonlinear Systems 322.6 Existence of Limit Cycles 362.7 Summary 382.8 Notes and References 382.9 Exercises 38VI113. Fundamentals of Lyapunov Theory 403.1 Nonlinear Systems and Equilibrium Points 413.2 Concepts of Stability 473.3 Linearization and Local Stability 533.4 Lyapunov's Direct Method 573.4.1 Positive Definite Functions and Lyapunov Functions 583.4.2 Equilibrium Point Theorems 613.4.3 Invariant Set Theorems 683.5 System Analysis Based on Lyapunov's Direct Method 763.5.1 Lyapunov Analysis of Linear Time-Invariant Systems 773.5.2 Krasovskii's Method 833.5.3 The Variable Gradient Method 863.5.4 Physically Motivated Lyapunov Functions 883.5.5 Performance Analysis 913.6 Control Design Based on Lyapunov's Direct Method 943.7 Summary 953.8 Notes and References 963.9 Exercises 974. Advanced Stability Theory 1004.1 Concepts of Stability for Non-Autonomous Systems 1014.2 Lyapunov Analysis of Non-Autonomous Systems 1054.2.1 Lyapunov's Direct Method for Non-Autonomous Systems 1054.2.2 Lyapunov Analysis of Linear Time-Varying Systems 1144.2.3 The Linearization Method for Non-Autonomous Systems 1164.3 * Instability Theorems 1174.4 * Existence of Lyapunov Functions 1204.5 Lyapunov-Like Analysis Using Barbalat's Lemma 1224.5.1 Asympt...
