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Chapter 1 Introduction to Control Theory
1£®1 Historical Review and Classical Control Theory
1£®1£®1 Historical Review of Automatic Control
1£®1£®2 Classical control theory
1£®2 Modern Control Theory
1£®3 Design of Control Systems
1£®4 Outline of This Book

Chapter 2 Preliminary Mathematical Knowledge
2£®1 Foundations of matrix algebra
2£®1£®1 Matrices
2£®1£®2 Algebraic operations with matrices
2£®1£®3 Matrix Operations
2£®2 Vectors and Vector Spaces
2£®2£®1 Vector
2£®2£®2 Vector Spaces and Subspaces
2£®3 Linear Algebra
2£®3£®1 Eigenvalue and Eigenvector of A Square Matrix
2£®3£®2 Linear Algebraic Equations
2£®3£®3 Similarity Transformation
2£®3£®4 Diagonal Form and Jordan Form
2£®3£®5 Cayley-Hamiton Theorem
2£®3£®6 Definiteness of A Scalar Function and Quadratic Form
Exercises

Chapter 3 State Variables and the State-Space Description of Dynamic Systems
3£®1 State-Space Representation of Dynamic Systems
3£®1£®1 State and State Variables
3£®1£®2 State-Space Representation
3£®1£®3 Block Diagrams and Simulation Diagrams
3£®2 Obtaining State Equations
3£®2£®1 From the Block Diagram
3£®2£®2 From Input-Output Representation
3£®2£®3 Equivalence Transformation of State-Space Representation
3£®3 Transfer Function And Realizations
3£®4 State-Space Representation of Linear Discrete-Time Systems
3£®5 Summaries
Exercises
Problems

Chapter 4 Time Response of Linear Systems
4£®1 Solution of LTI State Equations
4£®1£®1 Linear Homogeneous State Equations
4£®1£®2 The State Transition Matrix
4£®1£®3 Linear Nonhomogeous State Equations
4£®2 Numerical Solution of State Equations
4£®3 Solution of Linear Discrete-Time State Equations
4£®4 Discretization of Continuous-Time Systems
Exercises
Problems

Chapter 5 Controllability and Observability
5£®1 Corollaries of Cayley-Hamilton Theorem
5£®2 Controllability and Observability of LTI Systems
5£®2£®1 Controllability Definition and Rank Criterion
5£®2£®2 Observability Definition and Rank Criterion
5£®2£®3 Controllable Canonical Form and Observable Canonical Form
5£®2£®4 Principle of Duality
5£®3 Structural Decomposition of LTI systems
5£®4 Controllability£¬ Observability and Transfer Function
5£®5 Controllability and Observability of Discrete-Time Systems
5£®5£®1 Controllability of Discrete-Time Systems
5£®5£®2 Observability of Discrete-Time Systems
5£®5£®3 Controllability and Observability After Sampling
Exercises
Problems

Chapter 6 Lyapunov Stability
6£®1 Preliminary Examples
6£®2 Stability Concepts
6£®2£®1 Equilibrium State
6£®2£®2 Stability Definitions
6£®3 First Method of Lyapunov
6£®3£®1 Eigenvalue Criterion for Linear Time-invariant System
6£®3£®2 Eigenvalue Criterion for Linearized Time-invariant Systems
6£®4 Second Method of Lyapunov
6£®5 Lyapunov Equation
Exercise
Problems

Chapter 7 State Feedback and State Observer
7£®1 State Feedback and Output Feedback
7£®1£®1 State Feedback
7£®1£®2 Output Feedback
7£®2 Pole Placement using State feedback
7£®3 Pole placement using Output Feedback
7£®4 State Observer
7£®4£®1 Full-Dimensional Observer
7£®4£®2 Reduced-Dimensional State Observer
7£®5 Feedback From Estimated States
7£®6 The Engineering Applications of State Feedback and Observer
7£®6£®1 State Feedback Controller Design For The Inverted Pendulum
7£®6£®2 Asymptotic Tracking And Disturbance Rejection
7£®6£®3 System Stabilization
7£®6£®4 System Decoupling
Exercises
Problems

Chapter 8 Optimal Control
8£®1 Problem Formulation
8£®2 Preliminaries£ºThe extremum problem of functional
8£®2£®1 Functional and The Calculus of Variation
8£®2£®2 The Extremum Problem of Functional Without Constraints
8£®3 The Variational Approach to Optimal Control Problems
8£®4 Minimum Principle and Its Application
8£®4£®1 Pontryagin's Minimum Principle
8£®4£®2 Application of Minimum Principle
Exercises
Problems

Answers to Selected Exercises
Experiment 1£º Modeling and Stability Analysis of the Inverted Pendulum System
Experiment 2£º Design State Feedback Controller for the Inverted Pendulum System
Bibliography