About theAuthor ............................................ III
Preface..................................................... V
Notations................................................... VII
CHAPTER 1
Introduction................................................. 1
1.1 TheFirst Part: Finite Iterative Algorithm to Linear Matrix Equation . 1
1.2 TheSecond Part: MCGLS Iterative Algorithm to Linear Matrix
Equation............................................... 3
1.3 TheThird Part: Explicit Solutions to Linear Matrix Equation ...... 5
CHAPTER 2
FiniteIterative Algorithm to Coupled Transpose Matrix Equations ....... 11
2.1 FiniteIterative Algorithm and Convergence Analysis ............. 12
2.2Numerical Example ....................................... 24
2.3 ControlApplication ...................................... 27
2.4Conclusions............................................. 28
CHAPTER 3
FiniteIterative 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
3.3Numerical Example ....................................... 42
3.4 ControlApplication ...................................... 53
3.5Conclusions............................................. 54
CHAPTER 4
MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55
4.1 MCGLSIterative Algorithm and Convergence Analysis............ 57
4.2Numerical Example ....................................... 66
4.3 ControlApplication ...................................... 73
4.4Conclusions............................................. 74
CHAPTER 5
MCGLSIterative Algorithm to Linear Conjugate Transpose Matrix
Equation................................................... 75
5.1 MCGLSIterative Algorithm and Convergence Analysis............ 78
5.2Numerical Example ....................................... 90
5.3Conclusions............................................. 95
CHAPTER 6
MCGLSIterative Algorithm to Coupled Linear Operator Systems ........ 97
6.1 SomeUseful Lemmas ..................................... 98
6.2 MCGLSIterative Algorithm and Convergence Analysis............ 99
6.3Numerical Examples ...................................... 107
6.4Conclusions............................................. 113
CHAPTER 7
ExplicitSolutions to the Matrix Equation X − AXB = CY + R .......... 115
7.1 Solutionsto the Real Matrix Equation X − AXB = CY + R ....... 115
7.2Parametric Pole Assignment for Descriptor Linear Systems
by P-DFeedback ........................................ 124
7.3Conclusions............................................. 128
CHAPTER 8
ExplicitSolutions to the Nonhomogeneous Yakubovich-Transpose Matrix
Equation................................................... 131
8.1 TheFirst Approach ...................................... 132
8.2 TheSecond Approach ..................................... 140
8.3Illustrative Example ...................................... 142
8.4Conclusions............................................. 143
CHAPTER 9
ExplicitSolutions to the Matrix Equations XB
AXb ¼ CY.......................................... 145
9.1 RealMatrix Equation XB − AX = CY ........................ 145
9.2 Quaternion-j-Conjugate Matrix Equation XB − AXb = CY......... 148
9.2.1 RealRepresentation of a Quaternion Matrix .............. 148
9.2.2Solutions to the Quaternion j-Conjugate Matrix Equation
XB − AXb =CY ................................... 150
9.3Conclusions............................................. 155
X Contents
CHAPTER 10
ExplicitSolutions to Linear Transpose Matrix Equation ................ 157
10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157
10.1.1 TheFirst Case: A or B is Nonsingular ................. 158
10.1.2 TheSecond Case: A and B are Nonsingular ............. 162
10.2 Solutionsto the Generalized Sylvester Transpose Matrix Equation . . 165
10.3Algorithms for Solving Two Transpose Equations and Numerical
Example.............................................. 168
10.4Application in Control Theory ............................. 174
10.5Conclusions ............................................ 175
References.................................................. 177
