LEADER 05257nam 2200637Ia 450 001 9910458397803321 005 20200520144314.0 010 $a1-281-17210-3 010 $a9786611172107 010 $a0-08-055610-8 035 $a(CKB)1000000000393234 035 $a(EBL)330235 035 $a(OCoLC)808677269 035 $a(SSID)ssj0000097751 035 $a(PQKBManifestationID)11121623 035 $a(PQKBTitleCode)TC0000097751 035 $a(PQKBWorkID)10131931 035 $a(PQKB)10840918 035 $a(MiAaPQ)EBC330235 035 $a(Au-PeEL)EBL330235 035 $a(CaPaEBR)ebr10209709 035 $a(CaONFJC)MIL117210 035 $a(EXLCZ)991000000000393234 100 $a20071105d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDeterministic techniques$b[electronic resource] /$fAlexander S. Poznyak 210 $aAmsterdam $cElsevier$d2008- 215 $a1 online resource (803 p.) 225 0 $aAdvanced mathematical tools for automatic control engineers ;$v1 300 $aIncludes index. 311 $a0-08-044674-4 327 $aFront Cover; Advanced Mathematical Tools for Automatic Control Engineers; Copyright Page; Table of Contents; Preface; Notations and Symbols; List of Figures; Part I: Matrices and Related Topics; Chapter 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; Chapter 2. Matrices and Matrix Operations; 2.1 Basic Definitions; 2.2 Some Matrix Properties; 2.3 Kronecker Product; 2.4 Submatrices, Partitioning of Matrices and Schur's Formulas; 2.5 Elementary Transformations on Matrices 327 $a2.6 Rank of a Matrix2.7 Trace of a Quadratic Matrix; Chapter 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 and Generalized Eigenvectors; Chapter 4. Matrix Transformations; 4.1 Spectral Theorem for Hermitian Matrices; 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; Chapter 5. Matrix Functions; 5.1 Projectors; 5.2 Functions of a Matrix 327 $a5.3 The Resolvent for a Matrix5.4 Matrix Norms; Chapter 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 Pseudoinverse Matrices; 6.5 Solution of Least Squares Problem Using Pseudoinverse; 6.6 Cline's Formulas; 6.7 Pseudo-Ellipsoids; Chapter 7. Hermitian and Quadratic Forms; 7.1 Definitions; 7.2 Nonnegative Definite Matrices; 7.3 Sylvester Criterion; 7.4 The Simultaneous Transformation of a Pair of Quadratic Forms; 7.5 Simultaneous Reduction of more than Two Quadratic Forms 327 $a7.6 A Related Maximum-Minimum Problem7.7 The Ratio of Two Quadratic Forms; Chapter 8. Linear Matrix Equations; 8.1 General Type of Linear Matrix Equation; 8.2 Sylvester Matrix Equation; 8.3 Lyapunov Matrix Equation; Chapter 9. Stable Matrices and Polynomials; 9.1 Basic Definitions; 9.2 Lyapunov Stability; 9.3 Necessary Condition of the Matrix Stability; 9.4 The Routh-Hurwitz Criterion; 9.5 The Lie?nard-Chipart Criterion; 9.6 Geometric Criteria; 9.7 Polynomial Robust Stability; 9.8 Controllable, Stabilizable, Observable and Detectable Pairs; Chapter 10. Algebraic Riccati Equation 327 $a10.1 Hamiltonian Matrix10.2 All Solutions of the Algebraic Riccati Equation; 10.3 Hermitian and Symmetric Solutions; 10.4 Nonnegative Solutions; Chapter 11. Linear Matrix Inequalities; 11.1 Matrices as Variables and LMI Problem; 11.2 Nonlinear Matrix Inequalities Equivalent to LMI; 11.3 Some Characteristics of Linear Stationary Systems (LSS); 11.4 Optimization Problems with LMI Constraints; 11.5 Numerical Methods for LMI Resolution; Chapter 12. Miscellaneous; 12.1 Lambda-Matrix Inequalities; 12.2 Matrix Abel Identities; 12.3 S-Procedure and Finsler Lemma; 12.4 Farkas? Lemma 327 $a12.5 Kantorovich Matrix Inequality 330 $aThis 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 A 606 $aAutomatic control$xMathematics 606 $aMathematics 608 $aElectronic books. 615 0$aAutomatic control$xMathematics. 615 0$aMathematics. 676 $a629.8312 700 $aPoznyak$b Alexander S$0919961 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458397803321 996 $aDeterministic techniques$92130806 997 $aUNINA