Preface

Chapter 1. Introduction
1.1. Introduction
1.2. Overview
1.2.1. A Brief History

Chapter 2. Mathematical Descriptions of Systems
2.1. Introduction
2.2. Causality, Lumpedness, and Time Invariance
2.2.1. Impulses
2.3. Linear Time-Invariant Systems
2.3.1. Multi-input Multi-output Case
2.4. Linear Time-Varying Systems
2.4.1. Linearization
2.5. RLC Circuits-Comparisons of Various Descriptions
2.6. Mechanical and Hydraulic Systems
2.7. Proper Rational Transfer Functions
2.8. Discrete-Time Linear Time-Invariant Systems
2.9. Concluding Remarks -- Problems

Chapter 3. Linear Algebra
3.1. Introduction
3.2. Basis, Representation, and Orthonormalization
3.3. Linear Algebraic Equations
3.4. Similarity Transformation
3.5. Diagonal Form and Jordan Form
3.6. Functions of a Square Matrix
3.7. Lyapunov Equation
3.8. Some Useful Formulas
3.9. Quadratic Form and Positive Definiteness
3.10. Singular Value Decomposition
3.11. Norms of Matrices
Problems

Chapter 4. State-Space Solutions and Realizations
4.1. Introduction
4.2. General Solution of CT LTI State-Space Equations
4.2.1. Discretization
4.2.2. General Solution of DT LIT State-Space Equations
4.3. Computer Computation of CT State-Space Equations
4.3.1. Real-Time Processing
4.3.2. Op-Amp Circuit Implementation
4.4. Equivalent State-Space Equations
4.4.1. Canonical Forms
4.4.2. Magnitude Scaling in Op-Amp Circuits
4.5. Realizations
4.5.1. Multi-input Multi-output Case
4.6. Solution of Linear Time-Varying (LTV) Equations
4.6.1. Discrete-Time Case
4.7. Equivalent Time-Varying Equations
4.8. Time-Varying Realizations
Problems

Chapter 5. Stability
5.1. Introduction
5.2. Input-Output Stability of LTT Systems
5.3. Discrete-Time Case
5.4. Internal Stability
5.4.1. Discrete-Time Case
5.5. Lyapunov Theorem
5.5.1. Discrete-Time Case
5.6. Stability of LTV Systems
Problems

Chapter 6. Controllability and Observability
6.1. Introduction
6.2. Controllability
6.2.1. Controllability Indices
6.3. Observability
6.3.1. Observability Indices
6.4. Kalman Decomposition
6.5. Conditions in Jordan-Form Equations
6.6. Discrete-Time State-Space Equations
6.6.1. Controllability to the Origin and Reachability
6.7. Controllability after Sampling
6.8. LTV State-Space Equations
Problems

Chapter 7. Minimal Realizations and Coprime Fractions
7.1. Introduction
7.2. Implications of Coprimeness
7.2.1. Minimal Realizations
7.2.2. Complete Characterization
7.3. Computing Coprime Fractions
7.3.1. QR Decomposition
7.4. Balanced Realization
7.5. Realizations from Markov Parameters
7.6. Degree of Transfer Matrices
7.7. Minimal Realizations-Matrix Case
7.8. Matrix Polynomial Fractions
7.8.1. Column and Row Reducedness
7.8.2. Computing Matrix Coprime Fractions
7.9. Realization from Matrix Coprime Fractions
7.10. Realizations from Matrix Markov Parameters
7.11. Concluding Remarks
Problems

Chapter 8. State Feedback and State Estimators
8.1. Introduction
8.2. State Feedback
8.2.1. Solving Lyapunov Equation
8.3. Regulation and Tracking
8.3.1. Robust Tracking and Disturbance Rejection
8.3.2. Stabilization
8.4. State Estimator
8.4.1. Reduced-Dimensional State Estimator
8.5. Feedback from Estimated States
8.6. State Feedback-MLMO Case
8.6.1. Cyclic Design
8.6.2. Lyapunov-Equation Method
8.6.3. Controllable-Form Method
8.6.4. Effect on Transfer Matrices
8.7. State Estimators-MLMO Case
8.8. Feedback from Estimated States-MLMO Case
Problems

Chapter 9. Pole Placement and Model Matching
9.1. Introduction
9.2. Preliminary-Matching Coefficients
9.2.1. Compensator Equations-Classical Method
9.3. Unity-Feedback Configuration-Pole Placement
9.3.1. Regulation and Tracking
9.3.2. Robust Tracking and Disturbance Rejection
9.3.3. Embedding Internal Models
9.4. Implementable Transfer Functions
9.4.1. Model Matching-Two-Parameter Configuration
9.4.2. Implementation of Two-Parameter Compensators
9.5. MTMO Unity Feedback Systems
9.5.1. Regulation and Tracking
9.5.2. Robust Tracking and Disturbance Rejection
9.6. MTMO Model Matching-Two-Parameter Configuration
9.6.1. Decoupling
9.7. Concluding Remarks
Problems

References
Answers to Selected Problems
Index.