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Numerical Methods for Linear Control Systems.

By: Publisher: San Diego : Elsevier Science & Technology, 2004Copyright date: ©2003Edition: 1st edDescription: 1 online resource (736 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780080537887
Subject(s): Genre/Form: Additional physical formats: Print version:: Numerical Methods for Linear Control SystemsDDC classification:
  • 629.832
LOC classification:
  • QA402.3 -- .D368 2004eb
Online resources:
Contents:
Front Cover -- Numerical Methods For Linear Control Systems: Design and Analysis -- Copyright Page -- Contents -- Preface -- Acknowledgments -- About the Author -- List of Algorithms -- Notations and Symbols -- CHAPTER 1. INTRODUCTION AND OVERVIEW -- 1.1 Linear and Numerical Linear Algebra (Chapter 2 and Chapters 3 and 4) -- 1.2 System Responses (Chapter 5) -- 1.3 Controllability and Observability problems (Chapter 6) -- 1.4 Stability and Inertia (Chapter 7) -- 1.5 Lyapunov, Sylvester, and Algebraic Riccati Equations (Chapters 8 and 13) -- 1.6 Realization and Identification (Chapter 9) -- 1.7 Feedback Stabilization and Eigenvalue Assignment (Chapters 10 and 11) -- 1.8 State Estimation (Chapter 12) -- 1.9 Internal Balancing and Model Reduction (Chapter 14) -- 1.10 Nearness to Uncontrollability and Instability (Chapters 6 and 7) and Robust Stability and Stability Radius (Chapters 7 and 10) -- 1.11 Sensitivity and Condition Numbers of Control Problems -- 1.12 H∞ -Control (Chapter 10) -- 1.13 Software for Control Problems -- References -- PART I: REVIEW OF LINEAR AND NUMERICAL LINEAR ALGEBRA -- CHAPTER 2. A REVIEW OF SOME BASIC CONCEPTS AND RESULTS FROM THEORETICAL LINEAR ALGEBRA -- 2.1 Introduction -- 2.2 Orthogonality of Vectors and Subspaces -- 2.3 Matrices -- 2.4 Some Special Matrices -- 2.5 Vector and Matrix Norms -- 2.6 Norm Invariant Properties Under Unitary Matrix Multiplication -- 2.7 Kronecker Product, Kronecker Sum, and Vec Operation -- 2.8 Chapter Notes and Further Reading -- References -- CHAPTER 3. SOME FUNDAMENTAL TOOLS AND CONCEPTS FROM NUMERICAL LINEAR ALGEBRA -- 3.1 Introduction -- 3.2 Floating Point Numbers and Errors in Computations -- 3.3 Conditioning, Efficiency, Stability, and Accuracy -- 3.4 LU Factorization -- 3.5 Numerical Solution of the Linear System Ax=b -- 3.6 The QR Factorization.
3.7 Orthonormal Bases and Orthogonal Projections Using QR Factorization -- 3.8 The Least-Squares Problem -- 3.9 The Singular Value Decomposition (SVD) -- 3.10 Summary and Review -- 3.11 Chapter Notes and Further Reading -- References -- CHAPTER 4. CANONICAL FORMS OBTAINED VIA ORTHOGONAL TRANSFORMATIONS -- 4.1 Importance and Significance of Using Orthogonal Transformations -- 4.2 Hessenberg Reduction of a Matrix -- 4.3 The Real Schur Form of A: The QR Iteration Method -- 4.4 Computing the Singular Value Decomposition (SVD) -- 4.5 The Generalized Real Schur Form: The QZ algorithm -- 4.6 Computing of the Eigenvectors of the Pencil A - λB -- 4.7 Summary and Review -- 4.8 Chapter Notes and Further Reading -- References -- PART II: CONTROL SYSTEMS ANALYSIS -- CHAPTER 5. LINEAR STATE-SPACE MODELS AND SOLUTIONS OF THE STATE EQUATIONS -- 5.1 Introduction -- 5.2 State-Space Representations of Control Systems -- 5.3 Solutions of a Continuous-Time System: System Responses -- 5.4 State-Space Solution of the Discrete-Time System -- 5.5 Transfer Function and Frequency Response -- 5.6 Some Selected Software -- 5.7 Summary and Review -- 5.8 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 6. CONTROLLABILITY, OBSERVABILITY, AND DISTANCE TO UNCONTROLLABILITY -- 6.1 Introduction -- 6.2 Controllability: Definitions and Basic Results -- 6.3 Observability: Definitions and Basic Results -- 6.4 Decompositions of Uncontrollable and Unobservable Systems -- 6.5 Controller- and Observer-Canonical Forms -- 6.6 Numerical Difficulties with theoretical criteria of controllability and observability -- 6.7 A Numerically Effective Test of Controllability -- 6.8 A Numerically Effective Test of Observability -- 6.9 Distance to an Uncontrollable System -- 6.10 Distance to Uncontrollability and the Singular values of the Controllability Matrix.
6.11 Some Selected Software -- 6.12 Summary and Review -- 6.13 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 7. STABILITY, INERTIA, AND ROBUST STABILITY -- 7.1 Introduction -- 7.2 Stability of a Continuous-time System -- 7.3 Stability of a Discrete-time System -- 7.4 Some Inertia Theorems -- 7.5 Determining the Stability and Inertia of a Nonsymmetric Matrix -- 7.6 Distance to an Unstable System -- 7.7 Robust Stability -- 7.8 The Structured Stability Radius -- 7.9 Some Selected Software -- 7.10 Summary and Review -- 7.11 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 8. NUMERICAL SOLUTIONS AND CONDITIONING OF LYAPUNOV AND SYLVESTER EQUATIONS -- 8.1 Introduction -- 8.2 The Existence and Uniqueness of Solutions -- 8.3 Perturbation Analysis and the Condition Numbers -- 8.4 Analytical Methods for the Lyapunov Equations: Explicit Expressions for Solutions -- 8.5 Numerical Methods for the Lyapunov and Sylvester Equations -- 8.6 Direct Computations of the Cholesky Factors of Symmetric Positive Definite Solutions of Lyapunov Equations -- 8.7 Comparisions of Different Methods and Conclusions -- 8.8 Some Selected Software -- 8.9 Summary and Review -- 8.10 Chapter Notes and Further Reading -- Exercises -- References -- PART III: CONTROL SYSTEMS DESIGN -- CHAPTER 9. REALIZATION AND SUBSPACE IDENTIFICATION -- 9.1 Introduction -- 9.2 State-Space Realizations of a Transfer Function -- 9.3 Computing Minimal Realizations from Markov Parameters -- 9.4 Subspace Identification Algorithms -- 9.5 Some Selected Software -- 9.6 Summary and Review -- 9.7 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 10. FEEDBACK STABILIZATION, EIGENVALUE ASSIGNMENT, AND OPTIMAL CONTROL -- 10.1 Introduction -- 10.2 State-Feedback Stabilization -- 10.3 Detectability.
10.4 Eigenvalue and Eigenstructure Assignment Problems -- 10.5 The Quadratic Optimization Problems -- 10.6 H∞-Control Problems -- 10.7 The Complex Stability Radius and Riccati Equation -- 10.8 Some Selected Software -- 10.9 Summary and Review -- 10.10 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 11. NUMERICAL METHODS AND CONDITIONING OF THE EIGENVALUE ASSIGNMENT PROBLEMS -- 11.1 Introduction -- 11.2 Numerical Methods for the Single-input Eigenvalue Assignment Problem -- 11.3 Numerical Methods for the Multi-input Eigenvalue Assignment Problem -- 11.4 Conditioning of the Feedback Problem -- 11.5 Conditioning of the Closed-loop Eigenvalues -- 11.6 Robust Eigenvalue Assignment -- 11.7 Comparison of Efficiency and Stability" the Single-input EVA Problem -- 11.8 Comparison of Efficiency and Stability: the Multi-input EVA Problem -- 11.9 Comparative Discussion of Various Methods and Recommendation -- 11.10 Some Selected Software -- 11.11 Summary and Review -- 11.12 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 12. STATE ESTIMATION: OBSERVER AND THE KALMAN FILTER -- 12.1 Introduction -- 12.2 State Estimation via Eigenvalue Assignment -- 12.3 State Estimation via Sylvester Equation -- 12.4 Reduced-order State Estimation -- 12.5 Combined State Feedback and Observer Design -- 12.6 Characterization of Nonsingular Solutions of the Sylvester Equation -- 12.7 Numerical Solutions of the Sylvester-Observer Equation -- 12.8 Numerical Solutions of a Constrained Sylvester- observer Equation -- 12.9 Optimal State Estimation: The Kalman Filter -- 12.10 The Linear Quadratic Gaussian Problem -- 12.11 Some Selected Software -- 12.12 Summary and Review -- 12.13 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 13. NUMERICAL SOLUTIONS AND CONDITIONING OF ALGEBRAIC RICCATI EQUATIONS -- 13.1 Introduction.
13.2 The Existence and Uniqueness of the Stabilizing Solution of the CARE -- 13.3 The Existence and Uniqueness of the Stabilizing Solution of the DARE -- 13.4 Conditioning of the Riccati Equations -- 13.5 Computational Methods for Riccati Equations -- 13.6 The Schur and Inverse-Free Generalized Schur Methods for the Descriptor Riccati Equations -- 13.7 Conclusions and Table of Comparisons -- 13.8 Some Selected Software -- 13.9 Summary and Review -- 13.10 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 14. INTERNAL BALANCING AND MODEL REDUCTION -- 14.1 Introduction -- 14.2 Internal Balancing for Continuous-time Systems -- 14.3 Internal Balancing for Discrete-time Systems -- 14.4 Model Reduction -- 14.5 Hankel-Norm Approximations -- 14.6 Model Reduction of an Unstable System -- 14.7 Frequency-Weighted Model Reduction -- 14.8 Summary and Comparisons of Model Reduction Procedures -- 14.9 Some Selected Software -- 14.10 Summary and Review -- 14.11 Chapter Notes and Further Reading -- Exercises -- References -- PART IV: SPECIAL TOPICS -- CHAPTER 15. LARGE-SCALE MATRIX COMPUTATIONS IN CONTROL: KRYLOV SUBSPACE METHODS -- 15.1 Introduction -- 15.2 The Arnoldi and Block Arnoldi Methods -- 15.3 Scopes of using the Krylov Subspace Methods in Control -- 15.4 Arnoldi Methods for Lyapunov, Sylvester, and Algebraic Riccati Equations -- 15.5 Arnoldi Method for Partial Eigenvalue Assignment -- 15.6 Lanczos and Arnoldi Methods for Model Reduction -- 15.7 Chapter Notes and Further Reading -- Research Problems -- References -- APPENDIX A. SOME EXISTING SOFTWARE FOR CONTROL SYSTEMS DESIGN AND ANALYSIS -- A.1 MATLAB CONTROL SYSTEM TOOLBOX -- A.2 MATCONTROL -- A.3 Control System Professional-Advanced Numerical Methods (CSP-ANM) -- A.4 SLICOT -- A.5 MATRIX -- A.6 System Identification Software -- References.
APPENDIX B. MATCONTROL AND LISTING OF MATCONTROL FILES.
Summary: Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. MATLAB-based software is included for implementing all of the major algorithms from the book. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples Includes MATLAB-based solution software.
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Front Cover -- Numerical Methods For Linear Control Systems: Design and Analysis -- Copyright Page -- Contents -- Preface -- Acknowledgments -- About the Author -- List of Algorithms -- Notations and Symbols -- CHAPTER 1. INTRODUCTION AND OVERVIEW -- 1.1 Linear and Numerical Linear Algebra (Chapter 2 and Chapters 3 and 4) -- 1.2 System Responses (Chapter 5) -- 1.3 Controllability and Observability problems (Chapter 6) -- 1.4 Stability and Inertia (Chapter 7) -- 1.5 Lyapunov, Sylvester, and Algebraic Riccati Equations (Chapters 8 and 13) -- 1.6 Realization and Identification (Chapter 9) -- 1.7 Feedback Stabilization and Eigenvalue Assignment (Chapters 10 and 11) -- 1.8 State Estimation (Chapter 12) -- 1.9 Internal Balancing and Model Reduction (Chapter 14) -- 1.10 Nearness to Uncontrollability and Instability (Chapters 6 and 7) and Robust Stability and Stability Radius (Chapters 7 and 10) -- 1.11 Sensitivity and Condition Numbers of Control Problems -- 1.12 H∞ -Control (Chapter 10) -- 1.13 Software for Control Problems -- References -- PART I: REVIEW OF LINEAR AND NUMERICAL LINEAR ALGEBRA -- CHAPTER 2. A REVIEW OF SOME BASIC CONCEPTS AND RESULTS FROM THEORETICAL LINEAR ALGEBRA -- 2.1 Introduction -- 2.2 Orthogonality of Vectors and Subspaces -- 2.3 Matrices -- 2.4 Some Special Matrices -- 2.5 Vector and Matrix Norms -- 2.6 Norm Invariant Properties Under Unitary Matrix Multiplication -- 2.7 Kronecker Product, Kronecker Sum, and Vec Operation -- 2.8 Chapter Notes and Further Reading -- References -- CHAPTER 3. SOME FUNDAMENTAL TOOLS AND CONCEPTS FROM NUMERICAL LINEAR ALGEBRA -- 3.1 Introduction -- 3.2 Floating Point Numbers and Errors in Computations -- 3.3 Conditioning, Efficiency, Stability, and Accuracy -- 3.4 LU Factorization -- 3.5 Numerical Solution of the Linear System Ax=b -- 3.6 The QR Factorization.

3.7 Orthonormal Bases and Orthogonal Projections Using QR Factorization -- 3.8 The Least-Squares Problem -- 3.9 The Singular Value Decomposition (SVD) -- 3.10 Summary and Review -- 3.11 Chapter Notes and Further Reading -- References -- CHAPTER 4. CANONICAL FORMS OBTAINED VIA ORTHOGONAL TRANSFORMATIONS -- 4.1 Importance and Significance of Using Orthogonal Transformations -- 4.2 Hessenberg Reduction of a Matrix -- 4.3 The Real Schur Form of A: The QR Iteration Method -- 4.4 Computing the Singular Value Decomposition (SVD) -- 4.5 The Generalized Real Schur Form: The QZ algorithm -- 4.6 Computing of the Eigenvectors of the Pencil A - λB -- 4.7 Summary and Review -- 4.8 Chapter Notes and Further Reading -- References -- PART II: CONTROL SYSTEMS ANALYSIS -- CHAPTER 5. LINEAR STATE-SPACE MODELS AND SOLUTIONS OF THE STATE EQUATIONS -- 5.1 Introduction -- 5.2 State-Space Representations of Control Systems -- 5.3 Solutions of a Continuous-Time System: System Responses -- 5.4 State-Space Solution of the Discrete-Time System -- 5.5 Transfer Function and Frequency Response -- 5.6 Some Selected Software -- 5.7 Summary and Review -- 5.8 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 6. CONTROLLABILITY, OBSERVABILITY, AND DISTANCE TO UNCONTROLLABILITY -- 6.1 Introduction -- 6.2 Controllability: Definitions and Basic Results -- 6.3 Observability: Definitions and Basic Results -- 6.4 Decompositions of Uncontrollable and Unobservable Systems -- 6.5 Controller- and Observer-Canonical Forms -- 6.6 Numerical Difficulties with theoretical criteria of controllability and observability -- 6.7 A Numerically Effective Test of Controllability -- 6.8 A Numerically Effective Test of Observability -- 6.9 Distance to an Uncontrollable System -- 6.10 Distance to Uncontrollability and the Singular values of the Controllability Matrix.

6.11 Some Selected Software -- 6.12 Summary and Review -- 6.13 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 7. STABILITY, INERTIA, AND ROBUST STABILITY -- 7.1 Introduction -- 7.2 Stability of a Continuous-time System -- 7.3 Stability of a Discrete-time System -- 7.4 Some Inertia Theorems -- 7.5 Determining the Stability and Inertia of a Nonsymmetric Matrix -- 7.6 Distance to an Unstable System -- 7.7 Robust Stability -- 7.8 The Structured Stability Radius -- 7.9 Some Selected Software -- 7.10 Summary and Review -- 7.11 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 8. NUMERICAL SOLUTIONS AND CONDITIONING OF LYAPUNOV AND SYLVESTER EQUATIONS -- 8.1 Introduction -- 8.2 The Existence and Uniqueness of Solutions -- 8.3 Perturbation Analysis and the Condition Numbers -- 8.4 Analytical Methods for the Lyapunov Equations: Explicit Expressions for Solutions -- 8.5 Numerical Methods for the Lyapunov and Sylvester Equations -- 8.6 Direct Computations of the Cholesky Factors of Symmetric Positive Definite Solutions of Lyapunov Equations -- 8.7 Comparisions of Different Methods and Conclusions -- 8.8 Some Selected Software -- 8.9 Summary and Review -- 8.10 Chapter Notes and Further Reading -- Exercises -- References -- PART III: CONTROL SYSTEMS DESIGN -- CHAPTER 9. REALIZATION AND SUBSPACE IDENTIFICATION -- 9.1 Introduction -- 9.2 State-Space Realizations of a Transfer Function -- 9.3 Computing Minimal Realizations from Markov Parameters -- 9.4 Subspace Identification Algorithms -- 9.5 Some Selected Software -- 9.6 Summary and Review -- 9.7 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 10. FEEDBACK STABILIZATION, EIGENVALUE ASSIGNMENT, AND OPTIMAL CONTROL -- 10.1 Introduction -- 10.2 State-Feedback Stabilization -- 10.3 Detectability.

10.4 Eigenvalue and Eigenstructure Assignment Problems -- 10.5 The Quadratic Optimization Problems -- 10.6 H∞-Control Problems -- 10.7 The Complex Stability Radius and Riccati Equation -- 10.8 Some Selected Software -- 10.9 Summary and Review -- 10.10 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 11. NUMERICAL METHODS AND CONDITIONING OF THE EIGENVALUE ASSIGNMENT PROBLEMS -- 11.1 Introduction -- 11.2 Numerical Methods for the Single-input Eigenvalue Assignment Problem -- 11.3 Numerical Methods for the Multi-input Eigenvalue Assignment Problem -- 11.4 Conditioning of the Feedback Problem -- 11.5 Conditioning of the Closed-loop Eigenvalues -- 11.6 Robust Eigenvalue Assignment -- 11.7 Comparison of Efficiency and Stability" the Single-input EVA Problem -- 11.8 Comparison of Efficiency and Stability: the Multi-input EVA Problem -- 11.9 Comparative Discussion of Various Methods and Recommendation -- 11.10 Some Selected Software -- 11.11 Summary and Review -- 11.12 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 12. STATE ESTIMATION: OBSERVER AND THE KALMAN FILTER -- 12.1 Introduction -- 12.2 State Estimation via Eigenvalue Assignment -- 12.3 State Estimation via Sylvester Equation -- 12.4 Reduced-order State Estimation -- 12.5 Combined State Feedback and Observer Design -- 12.6 Characterization of Nonsingular Solutions of the Sylvester Equation -- 12.7 Numerical Solutions of the Sylvester-Observer Equation -- 12.8 Numerical Solutions of a Constrained Sylvester- observer Equation -- 12.9 Optimal State Estimation: The Kalman Filter -- 12.10 The Linear Quadratic Gaussian Problem -- 12.11 Some Selected Software -- 12.12 Summary and Review -- 12.13 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 13. NUMERICAL SOLUTIONS AND CONDITIONING OF ALGEBRAIC RICCATI EQUATIONS -- 13.1 Introduction.

13.2 The Existence and Uniqueness of the Stabilizing Solution of the CARE -- 13.3 The Existence and Uniqueness of the Stabilizing Solution of the DARE -- 13.4 Conditioning of the Riccati Equations -- 13.5 Computational Methods for Riccati Equations -- 13.6 The Schur and Inverse-Free Generalized Schur Methods for the Descriptor Riccati Equations -- 13.7 Conclusions and Table of Comparisons -- 13.8 Some Selected Software -- 13.9 Summary and Review -- 13.10 Chapter Notes and Further Reading -- Exercises -- References -- CHAPTER 14. INTERNAL BALANCING AND MODEL REDUCTION -- 14.1 Introduction -- 14.2 Internal Balancing for Continuous-time Systems -- 14.3 Internal Balancing for Discrete-time Systems -- 14.4 Model Reduction -- 14.5 Hankel-Norm Approximations -- 14.6 Model Reduction of an Unstable System -- 14.7 Frequency-Weighted Model Reduction -- 14.8 Summary and Comparisons of Model Reduction Procedures -- 14.9 Some Selected Software -- 14.10 Summary and Review -- 14.11 Chapter Notes and Further Reading -- Exercises -- References -- PART IV: SPECIAL TOPICS -- CHAPTER 15. LARGE-SCALE MATRIX COMPUTATIONS IN CONTROL: KRYLOV SUBSPACE METHODS -- 15.1 Introduction -- 15.2 The Arnoldi and Block Arnoldi Methods -- 15.3 Scopes of using the Krylov Subspace Methods in Control -- 15.4 Arnoldi Methods for Lyapunov, Sylvester, and Algebraic Riccati Equations -- 15.5 Arnoldi Method for Partial Eigenvalue Assignment -- 15.6 Lanczos and Arnoldi Methods for Model Reduction -- 15.7 Chapter Notes and Further Reading -- Research Problems -- References -- APPENDIX A. SOME EXISTING SOFTWARE FOR CONTROL SYSTEMS DESIGN AND ANALYSIS -- A.1 MATLAB CONTROL SYSTEM TOOLBOX -- A.2 MATCONTROL -- A.3 Control System Professional-Advanced Numerical Methods (CSP-ANM) -- A.4 SLICOT -- A.5 MATRIX -- A.6 System Identification Software -- References.

APPENDIX B. MATCONTROL AND LISTING OF MATCONTROL FILES.

Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. MATLAB-based software is included for implementing all of the major algorithms from the book. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples Includes MATLAB-based solution software.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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