Symbol Descriptions
R
Real number field
R þ
Positive real number field
R
n
Set of n-dimensional real vectors
R
nÂm
Set of n  m-dimensional real matrices
I
Identity matrix
A [ ð ! ; \; Þ The matrix A is positive definite (positive semidefinite, negative
definite, negative semidefinite)
x
T
; A
T
Transposition of vector x or matrix A
A
À1
Inverse matrix of A
0
The number 0 or 0 matrix with appropriate dimensions
rðAÞ
Eigenvalues of matrix A
I
Weak infinitesimal (differential) operators
r
Gradient (difference) operator
P N
i;j a ij
Summation
Ã
Transpose matrix of the corresponding module in symmetric
matrix
EÁ
Mathematical expectation
diag Á Á Á
Diagonal matrix
col½Á Á Á
Column matrix
k Á k
Euclidean norm of vectors or universal norm of matrices
L 2 ½0; 1Þ
Time domain square integrable function space for continuous
systems
R c ; R d
Continuous probability space and discrete probability space
LMIðsÞ
Linear Matrix Inequality(ies)
xiii
R
Real number field
R þ
Positive real number field
R
n
Set of n-dimensional real vectors
R
nÂm
Set of n  m-dimensional real matrices
I
Identity matrix
A [ ð ! ; \; Þ The matrix A is positive definite (positive semidefinite, negative
definite, negative semidefinite)
x
T
; A
T
Transposition of vector x or matrix A
A
À1
Inverse matrix of A
0
The number 0 or 0 matrix with appropriate dimensions
rðAÞ
Eigenvalues of matrix A
I
Weak infinitesimal (differential) operators
r
Gradient (difference) operator
P N
i;j a ij
Summation
Ã
Transpose matrix of the corresponding module in symmetric
matrix
EÁ
Mathematical expectation
diag Á Á Á
Diagonal matrix
col½Á Á Á
Column matrix
k Á k
Euclidean norm of vectors or universal norm of matrices
L 2 ½0; 1Þ
Time domain square integrable function space for continuous
systems
R c ; R d
Continuous probability space and discrete probability space
LMIðsÞ
Linear Matrix Inequality(ies)
xiii