This book provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is includes proofs of all theorems and contains many examples with solutions.
It is written for researchers, engineers, and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to System and Automatic Control Theories
* Provides comprehensive theory of matrices, real, complex and functional analysis
* Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications
* Contains worked proofs of all theorems and propositions presented
1. Cover image - p. Cover 2. Title page - p. Cover 3. Table of Contents - p. Cover 4. Dedication - p. Cover 5. Copyright - p. ii 6. Preface - p. ii 7. Notations and Symbols - p. xx 8. List of Figures - p. xxvi 9. PART I: MATRICES AND RELATED TOPICS - p. xxviii 10. Chapter 1: Determinants - p. xxviii 11. Chapter 2: Matrices and Matrix Operations - p. 18 12. Chapter 3: Eigenvalues and Eigenvectors - p. 39 13. Chapter 4: Matrix Transformations - p. 57 14. Chapter 5: Matrix Functions - p. 75 15. Chapter 6: Moore–Penrose Pseudoinverse - p. 95 16. Chapter 7: Hermitian and Quadratic Forms - p. 114 17. Chapter 8: Linear Matrix Equations - p. 132 18. Chapter 9: Stable Matrices and Polynomials - p. 137 19. Chapter 10: Algebraic Riccati Equation - p. 174 20. Chapter 11: Linear Matrix Inequalities - p. 190 21. Chapter 12: Miscellaneous - p. 212 22. PART II: ANALYSIS - p. 227 23. Chapter 13: The Real and Complex Number Systems - p. 227 24. Chapter 14: Sets, Functions and Metric Spaces - p. 250 25. Chapter 15: Integration - p. 274 26. Chapter 16: Selected Topics of Real Analysis - p. 314 27. Chapter 17: Complex Analysis - p. 395 28. Chapter 18: Topics of Functional Analysis - p. 450 29. PART III: DIFFERENTIAL EQUATIONS AND OPTIMIZATION - p. 498 30. Chapter 19: Ordinary Differential Equations - p. 498 31. Chapter 20: Elements of Stability Theory - p. 559 32. Chapter 21: Finite-Dimensional Optimization - p. 599 33. Chapter 22: Variational Calculus and Optimal Control - p. 645 34. Chapter 23: H2 and H∞ Optimization - p. 711 35. BIBLIOGRAPHY - p. 762 36. INDEX - p. 765
This book provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is includes proofs of all theorems and contains many examples with solutions.
It is written for researchers, engineers, and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to System and Automatic Control Theories
* Provides comprehensive theory of matrices, real, complex and functional analysis
* Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications
* Contains worked proofs of all theorems and propositions presented
1. Cover image - p. Cover 2. Title page - p. Cover 3. Table of Contents - p. Cover 4. Dedication - p. Cover 5. Copyright - p. ii 6. Preface - p. ii 7. Notations and Symbols - p. xx 8. List of Figures - p. xxvi 9. PART I: MATRICES AND RELATED TOPICS - p. xxviii 10. Chapter 1: Determinants - p. xxviii 11. Chapter 2: Matrices and Matrix Operations - p. 18 12. Chapter 3: Eigenvalues and Eigenvectors - p. 39 13. Chapter 4: Matrix Transformations - p. 57 14. Chapter 5: Matrix Functions - p. 75 15. Chapter 6: Moore–Penrose Pseudoinverse - p. 95 16. Chapter 7: Hermitian and Quadratic Forms - p. 114 17. Chapter 8: Linear Matrix Equations - p. 132 18. Chapter 9: Stable Matrices and Polynomials - p. 137 19. Chapter 10: Algebraic Riccati Equation - p. 174 20. Chapter 11: Linear Matrix Inequalities - p. 190 21. Chapter 12: Miscellaneous - p. 212 22. PART II: ANALYSIS - p. 227 23. Chapter 13: The Real and Complex Number Systems - p. 227 24. Chapter 14: Sets, Functions and Metric Spaces - p. 250 25. Chapter 15: Integration - p. 274 26. Chapter 16: Selected Topics of Real Analysis - p. 314 27. Chapter 17: Complex Analysis - p. 395 28. Chapter 18: Topics of Functional Analysis - p. 450 29. PART III: DIFFERENTIAL EQUATIONS AND OPTIMIZATION - p. 498 30. Chapter 19: Ordinary Differential Equations - p. 498 31. Chapter 20: Elements of Stability Theory - p. 559 32. Chapter 21: Finite-Dimensional Optimization - p. 599 33. Chapter 22: Variational Calculus and Optimal Control - p. 645 34. Chapter 23: H2 and H∞ Optimization - p. 711 35. BIBLIOGRAPHY - p. 762 36. INDEX - p. 765
