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| Preface | |
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| Introduction | |
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| Introduction | |
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| Overview | |
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| A Brief History | |
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| Mathematical Descriptions of Systems | |
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| Introduction | |
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| Causality, Lumpedness, and Time Invariance | |
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| Impulses | |
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| Linear Time-Invariant Systems | |
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| Multi-input Multi-output Case | |
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| Linear Time-Varying Systems | |
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| Linearization | |
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| RLC Circuits-Comparisons of Various Descriptions | |
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| Mechanical and Hydraulic Systems | |
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| Proper Rational Transfer Functions | |
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| Discrete-Time Linear Time-Invariant Systems | |
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| Concluding Remarks | |
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| Problems | |
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| Linear Algebra | |
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| Introduction | |
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| Basis, Representation, and Orthonormalization | |
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| Linear Algebraic Equations | |
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| Similarity Transformation | |
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| Diagonal Form and Jordan Form | |
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| Functions of a Square Matrix | |
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| Lyapunov Equation | |
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| Some Useful Formulas | |
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| Quadratic Form and Positive Definiteness | |
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| Singular Value Decomposition | |
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| Norms of Matrices | |
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| Problems | |
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| State-Space Solutions and Realizations | |
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| Introduction | |
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| General Solution of CT LTI State-Space Equations | |
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| Discretization | |
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| General Solution of DT LIT State-Space Equations | |
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| Computer Computation of CT State-Space Equations | |
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| Real-Time Processing | |
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| Op-Amp Circuit Implementation | |
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| Equivalent State-Space Equations | |
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| Canonical Forms | |
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| Magnitude Scaling in Op-Amp Circuits | |
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| Realizations | |
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| Multi-input Multi-output Case | |
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| Solution of Linear Time-Varying (LTV) Equations | |
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| Discrete-Time Case | |
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| Equivalent Time-Varying Equations | |
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| Time-Varying Realizations | |
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| Problems | |
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| Stability | |
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| Introduction | |
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| Input-Output Stability of LTT Systems | |
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| Discrete-Time Case | |
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| Internal Stability | |
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| Discrete-Time Case | |
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| Lyapunov Theorem | |
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| Discrete-Time Case | |
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| Stability of LTV Systems | |
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| Problems | |
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| Controllability and Observability | |
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| Introduction | |
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| Controllability | |
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| Controllability Indices | |
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| Observability | |
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| Observability Indices | |
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| Kalman Decomposition | |
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| Conditions in Jordan-Form Equations | |
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| Discrete-Time State-Space Equations | |
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| Controllability to the Origin and Reachability | |
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| Controllability after Sampling | |
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| LTV State-Space Equations | |
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| Problems | |
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| Minimal Realizations and Coprime Fractions | |
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| Introduction | |
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| Implications of Coprimeness | |
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| Minimal Realizations | |
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| Complete Characterization | |
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| Computing Coprime Fractions | |
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| QR Decomposition | |
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| Balanced Realization | |
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| Realizations from Markov Parameters | |
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| Degree of Transfer Matrices | |
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| Minimal Realizations-Matrix Case | |
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| Matrix Polynomial Fractions | |
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| Column and Row Reducedness | |
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| Computing Matrix Coprime Fractions | |
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| Realization from Matrix Coprime Fractions | |
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| Realizations from Matrix Markov Parameters | |
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| Concluding Remarks | |
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| Problems | |
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| State Feedback and State Estimators | |
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| Introduction | |
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| State Feedback | |
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| Solving Lyapunov Equation | |
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| Regulation and Tracking | |
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| Robust Tracking and Disturbance Rejection | |
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| Stabilization | |
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| State Estimator | |
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| Reduced-Dimensional State Estimator | |
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| Feedback from Estimated States | |
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| State Feedback-MLMO Case | |
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| Cyclic Design | |
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| Lyapunov-Equation Method | |
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| Controllable-Form Method | |
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| Effect on Transfer Matrices | |
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| State Estimators-MLMO Case | |
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| Feedback from Estimated States-MLMO Case | |
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| Problems | |
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| Pole Placement and Model Matching | |
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| Introduction | |
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| Preliminary-Matching Coefficients | |
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| Compensator Equations-Classical Method | |
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| Unity-Feedback Configuration-Pole Placement | |
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| Regulation and Tracking | |
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| Robust Tracking and Disturbance Rejection | |
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| Embedding Internal Models | |
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| Implementable Transfer Functions | |
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| Model Matching-Two-Parameter Configuration | |
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| Implementation of Two-Parameter Compensators | |
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| MTMO Unity Feedback Systems | |
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| Regulation and Tracking | |
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| Robust Tracking and Disturbance Rejection | |
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| MTMO Model Matching-Two-Parameter Configuration | |
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| Decoupling | |
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| Concluding Remarks | |
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| Problems | |
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| References | |
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| Answers to Selected Problems | |
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| Index | |