Solutions to Linear Matrix Equations and Their Applications

About the Author ............................................ III

Preface..................................................... V

Notations................................................... VII

CHAPTER 1

Introduction................................................. 1

1.1 The First Part: Finite Iterative Algorithm to Linear Matrix Equation . 1

1.2 The Second Part: MCGLS Iterative Algorithm to Linear Matrix Equation............................................... 3

1.3 The Third Part: Explicit Solutions to Linear Matrix Equation ...... 5

CHAPTER 2

Finite Iterative Algorithm to Coupled Transpose Matrix Equations ....... 11

2.1 Finite Iterative Algorithm and Convergence Analysis ............. 12

2.2 Numerical Example ....................................... 24

2.3 Control Application ...................................... 27

2.4 Conclusions............................................. 28

CHAPTER 3

Finite Iterative Algorithm to Coupled Operator Matrix Equations withSub-Matrix Constrained .................................... 29

3.1Iterative Method for Solving Problem 3.1 ...................... 30

3.2Iterative Method for Solving Problem 3.2 ...................... 41

3.3 Numerical Example ....................................... 42

3.4 Control Application ...................................... 53

3.5 Conclusions............................................. 54

CHAPTER 4

MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55

4.1 MCGL SIterative Algorithm and Convergence Analysis............ 57

4.2 Numerical Example ....................................... 66

4.3 ControlApplication ...................................... 73

4.4 Conclusions............................................. 74

CHAPTER 5

MCGLS Iterative Algorithm to Linear Conjugate Transpose Matrix Equation................................................... 75

5.1 MCGLS Iterative Algorithm and Convergence Analysis............ 78

5.2 Numerical Example ....................................... 90

5.3 Conclusions............................................. 95

CHAPTER 6

MCGLS Iterative Algorithm to Coupled Linear Operator Systems ........ 97

6.1 Some Useful Lemmas ..................................... 98

6.2 MCGLS Iterative Algorithm and Convergence Analysis............ 99

6.3 Numerical Examples ...................................... 107

6.4 Conclusions............................................. 113

CHAPTER 7

Explicit Solutions to the Matrix Equation X − AXB = CY + R .......... 115

7.1 Solutions to the Real Matrix Equation X − AXB = CY + R ....... 115

7.2 Parametric Pole Assignment for Descriptor Linear Systems by P-DFeedback ........................................ 124

7.3 Conclusions............................................. 128

CHAPTER 8

Explicit Solutions to the Non homogeneous Yakubovich-Transpose Matrix Equation................................................... 131

8.1 The First Approach ...................................... 132

8.2 The Second Approach ..................................... 140

8.3 Illustrative Example ...................................... 142

8.4 Conclusions............................................. 143

CHAPTER 9

Explicit Solutions to the Matrix Equations XB-AX = CY.......................................... 145

9.1 Real Matrix Equation XB − AX = CY and XB - AX = CY  ........................ 145

9.2 Quaternion-j-Conjugate Matrix Equation XB − AX = CY......... 148

9.2.1 Real Representation of a Quaternion Matrix .............. 148

9.2.2 Solutions to the Quaternion j-Conjugate Matrix Equation XB − AX =CY ................................... 150

9.3 Conclusions............................................. 155

CHAPTER 10

Explicit Solutions to Linear Transpose Matrix Equation ................ 157

10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157

10.1.1 The First Case: A or B is Nonsingular ................. 158

10.1.2 The Second Case: A and B are Nonsingular ............. 162

10.2 Solutions to the Generalized Sylvester Transpose Matrix Equation . . 165

10.3 Algorithms for Solving Two Transpose Equations and Numerical Example.............................................. 168

10.4 Application in Control Theory ............................. 174

10.5 Conclusions ............................................ 175

References.................................................. 177

Langue(s) : Anglais

Public(s) : Professionnels, Recherche, Etudiants

Editeur : EDP Sciences & Science Press

Collection : Current Natural Sciences

Publication : 20 juillet 2023

EAN13 (papier) : 9782759831029

Référence eBook [PDF] : L31036

EAN13 eBook [PDF] : 9782759831036

Intérieur : Couleur, Noir & blanc

Nombre de pages eBook [PDF] : 196

Taille(s) : 2,82 Mo (PDF)