Advanced Mathematical Tools for Automatic Control Engineers 1

Advanced Mathematical Tools for Control Engineers: Volume 1 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

Table of Contents

Part I: Matrices and Related Topics

Chapter 1. Determinants

Chapter 2. Matrices and Matrix Operations

Chapter 3. Eigenvalues and Eigenvectors

Chapter 4. Matrix Transformations

Chapter 5. Matrix Functions

Chapter 6. Moore- Penrose Pseudoinverse

Chapter 7. Hermitian and Quadratic Forms

Chapter 8. Linear Matrix Equations

Chapter 9. Stable Matrices and Polynomials

Chapter 10. Algebraic Riccati Equation

Chapter 11. Linear Matrix Inequalities

Chapter 12. Miscellaneous

Part II: Analysis

Chapter 13. The Real and Complex Number Systems

Chapter 14. Sets, Functions and Metric Spaces

Chapter 15. Integration

Chapter 16. Selected Topics of Real Analysis

Chapter 17. Complex Analysis

Chapter 18. Topics of Functional Analysis

Part Ill: Differential Equations and Optimization

Chapter 19. Ordinary Differential Equations

Chapter 20. Elements of Stability Theory

Chapter 21. Finite-Dimensional Optimization

Chapter 22. Variational Calculus and Optimal Control

Chapter 23. H2 and H& Optimization

About the Author

Alexander Poznyak is Professor and Department Head of Automatic Control at CINESTAV of IPN in Mexico. He graduated from Moscow Physical Technical Institute in 1970, and earned Ph.D. and Doctoral Degrees from the Institute of Control Sciences of Russian Academy of Sciences in 1978 and 1989, respectively. He has directed 43 Ph.D. theses, and published more than 260 papers and 14 books.