Page 25 - Electrical Engineering Dictionary

n t common symbol for thermal noise in deux indices,” IRIA Rapport Laboria, No.
watts. 31, Sept. 1973.

10base2 a type of coaxial cable used to 2-D Fornasini–Marchesini model a 2-D
connect nodes on an Ethernet network. The model described by the equations
10 refers to the transfer rate used on standard
Ethernet, 10 megabits per second. The base x i+1,j+1 = A 0 x i,j + A 1 x i+1,j
means that the network uses baseband com- + A 2 x i,j+1 + Bu ij (1a)
munication rather than broadband communi- y ij = Cx ij + Du ij (1b)
cations, and the 2 stands for the maximum
length of cable segment, 185 meters (almost i, j ∈ Z + (the set of nonnegative integers)
n
200). This type of cable is also called “thin” here x ij ∈ R is the local state vector,
m
p
Ethernet, because it is a smaller diameter ca- u ij ∈ R is the input vector, y ij ∈ R is
ble than the 10base5 cables. the output vector A k (k = 0, 1, 2), B, C, D
are real matrices. A 2-D model described by
10base5 a type of coaxial cable used to the equations
connect nodes on an Ethernet network. The
10 refers to the transfer rate used on stan- x i+1,j+1 = A 1 x i+1,j + A 2 x i,j+1
dard Ethernet, 10 megabits per second. The + B 1 u i+1,j + B 2 u i,j+1 (2)
base means that the network uses baseband
i, j ∈ Z + and (1b) is called the second 2-D
communication rather than broadband com-
Fornasini–Marchesini model, where x ij , u ij ,
munications, and the 5 stands for the max-
and y ij are defined in the same way as for (1),
imum length of cable segment of approxi-
A k , B k (k = 0, 1, 2) are real matrices. The
mately 500 meters. This type of cable is also
model (1) is a particular case of (2).
called “thick” Ethernet, because it is a larger
diameter cable than the 10base2 cables.
2-D general model a 2-D model de-
scribed by the equations
10baseT a type of coaxial cable used to
connect nodes on an Ethernet network. The
x i+1,j+1 = A 0 x i,j + A 1 x i+1,j
10 refers to the transfer rate used on standard
+ A 2 x i,j+1 + B 0 u ij
Ethernet, 10 megabits per second. The base
means that the network uses baseband com- + B 1 u i+1,j + B 2 u i,j+1
munication rather than broadband communi- y ij = Cx ij + Du ij
cations, and the T stands for twisted (wire)
i, j ∈ Z + (the set of nonnegative integers)
cable.
n
here x ij ∈ R is the local state vector, u ij ∈
m
p
R is the input vector, y ij ∈ R is the output
2-D Attasi model a 2-D model described
vector and A k , B k (k = 0, 1, 2), C, D are real
by the equations
matrices. In particular case for B 1 = B 2 = 0
we obtain the first 2-D Fornasini–Marchesini
x i+1,j+1 =−A 1 A 2 x i,j + A 1 x i+1,j
model and for A 0 = 0 and B 0 = 0 we obtain
+ A 2 x i,j+1 + Bu ij
the second 2-D Fornasini–Marchesini model.
y ij = Cx ij + Du ij
2-D polynomial matrix equation a 2-D
i, j ∈ Z + (the set of nonnegative integers). equation of the form
Here x ij ∈ R n is the local state vector,
p
u ij ∈ R m is the input vector, y ij ∈ R is AX + BY = C (1)
the output vector, and A 1 , A 2 , B, C, D are
real matrices. The model was introduced by where A ∈ R k×p [s], B ∈ R k×q [s], C ∈
Attasi in “Systemes lineaires homogenes a R k×m [s] are given, by a solution to (1) we
c
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