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 also 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
Content:
Front Matter
• Preface
• Table of Contents
•Part I. Matrices and Related Topics 1. Determinants
2. Matrices and Matrix Operations
3. Eigenvalues and Eigenvectors
4. Matrix Transformations
5. Matrix Functions
6. Moore-Penrose Pseudoinverse
7. Hermitian and Quadratic Forms
8. Linear Matrix Equations
9. Stable Matrices and Polynomials
10. Algebraic Riccati Equation
11. Linear Matrix Inequalities
12. Miscellaneous
•Part II. Analysis 13. The Real and Complex Number Systems
14. Sets, Functions and Metric Spaces
15. Integration
16. Selected Topics of Real Analysis
17. Complex Analysis
18. Topics of Functional Analysis
•Part III. Differential Equations and Optimization 19. Ordinary Differential Equations
20. Elements of Stability Theory
21. Finite-Dimensional Optimization
22. Variational Calculus and Optimal Control
23. H2 and H∞ Optimization
• Bibliography
Index