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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 | |