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
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
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
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
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 811
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.
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