Advanced Mathematical Tools for Control Engineers: Volume 1

1st Edition

Deterministic Systems

Authors: Alex Poznyak
Hardcover ISBN: 9780080446745
eBook ISBN: 9780080556109
Imprint: Elsevier Science
Published Date: 17th December 2007
Page Count: 808
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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

Key Features

  • 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


Undergraduate, graduate, research students of automotive control engineering, aerospace engineering, mechanical engineering and control in Chemical engineering.

Table of Contents

I MATRICES AND RELATED TOPICS 1 1 Determinants 1.1 Basic definitions 1.2 Properties of numerical determinants, minors and cofactors 1.3 Linear algebraic equations and the existence of solutions 2 Matrices and Matrix Operations 2.1 Basic definitions
2.2 Somematrix properties 2.3 Kronecker product 2.4 Submatrices, partitioning of matrices and Schur’s formulas 2.5 Elementary transformations onmatrices 2.6 Rank of a matrix 2.7 Trace of a quadraticmatrix 3 Eigenvalues and Eigenvectors 3.1 Vectors and linear subspaces 3.2 Eigenvalues and eigenvectors 3.3 The Cayley-Hamilton theorem 3.4 The multiplicities of an eigenvalue and generalized eigenvectors 4 Matrix Transformations 4.1 Spectral theorem for hermitianmatrices 4.1.1 Eigenvectors of a multiple eigenvalue for hermitianmatrices 4.2 Matrix transformation to the Jordan form 4.3 Polar and singular-value decompositions 4.4 Congruent matrices and the inertia of a matrix 4.5 Cholesky factorization 5 Matrix Functions 5.1 Projectors 5.2 Functions of a matrix 5.3 The resolvent formatrix 5.4 Matrix norms 6 Moore-Penrose Pseudoinverse 6.1 Classical Least Squares Problem 6.2 Pseudoinverse characterization 6.3 Criterion for pseudoinverse checking 6.4 Some identities for pseudoinversematrices 6.5 Solution of Least Square Problem using pseudoinverse 6.6 Cline’s formulas 6.7 Pseudo-ellipsoids

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About the Author

Alex Poznyak

Alexander S. Poznyak has published more than 200 papers in different international journals and 13 books including 2 for Elsevier. He is Fellow of IMA (Institute of Mathematics and Its Applications, Essex UK) and Associated Editor of Oxford-IMA Journal on Mathematical Control and Information. He was also Associated Editor of CDC, ACC and Member of Editorial Board of IEEE CSS. He is a member of the Evaluation Committee of SNI (Ministry of Science and Technology) responsible for Engineering Science and Technology Foundation in Mexico, and a member of Award Committee of Premium of Mexico on Science and Technology. In 2014 he was invited by the USA Government to serve as the member of NSF committee on “Neuro Sciences and Artificial Intelligence”.

Affiliations and Expertise

Professor in Automatic Control at CINVESTAV-IPN, Mexico