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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© 2008
Elsevier Science
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