Page 131 - Electrical Engineering Dictionary

m
p(z 1 ,z 2 ) = 0 is called the 2-D character- R is the input vector, and A k ,B k (k = 1, 2)
istic equation of the model. are real matrices.
p(z 1 ,z 2 ) = 0 is called the 2-D character-
characteristic polynomial assignment of istic equation of the model.
2-D Roesser model consider the 2-D
Roesser model characteristic polynomial of 2-D Roesser
model the determinant
" h # " h #
x x
i+1,j = A 1 A 2 ij + B 1 z
x v A 3 A 4 x v B 2 u ij p (z 1 ,z 2 ) = det I n 1 1 − A 1 −A 2
i,j+1 ij
z
−A 3 I n 2 2 − A 4
i, j ∈ Z + (the set of nonnegative integers) n 1 n 2
X X i j
with the state-feedback = a ij z z a n 1 2 = 1
n
1 2
" h # i=0 j=0
x ij
u ij = K v + v ij is called the 2-D characteristic polynomial of
x
ij
the 2-D Roesser model
v
h
n 1
where x ∈ R , and x ∈ R n 2 are the hori- " # " #
ij ij h h
zontal and vertical state vectors, respectively, x i+1,j = A 1 A 2 x ij v + B 1 u ij
v
m
u ij ∈ R is the input vector, and A 1 , A 2 , A 3 , x i,j+1 A 3 A 4 x ij B 2
A 4 , B 1 , B 2 are real matrices of the model,
i, j ∈ Z + (the set of nonnegative integers)
h
v
n 1
ij
K = [K 1 ,K 2 ] ∈ R m×(n 1 +n 2 ) where x ∈ R , and x ∈ R n 2 are the hori-
ij
zontal and vertical state vectors, respectively,
m
m
and v ij ∈ R is a new input vector. Given the u ij ∈ R is the input vector, and A 1 , A 2 , A 3 ,
model and a desired 2-D characteristic poly- A 4 , B 1 , B 2 are real matrices.
nomial of the closed-loop system p c (z 1 ,z 2 ), p(z 1 ,z 2 ) = 0 is called the 2-D character-
find a gain feedback matrix K such that istic equation of the model.

z
I n 1 1 − A 1 − B 1 K 1 −A 2 − B 1 K 2 characterization the process of cal-
det
z
−A 3 − B 2 K 1 I n 2 2 − A 4 − B 2 K 2
ibrating test equipment, measuring, de-
embedding and evaluating a component or
n 1 n 2
X X i j circuit for DC RF and/or digital performance.
= p c (z 1 ,z 2 ) = d ij z z d n 1 n 2 = 1
1 2
i=0 j=0 charge a basic physical quantity that is a
source of electromagnetic fields.
characteristicpolynomialof2-DFornasini–
charge carrier a unit of electrical charge
Marchesini model the determinant
that when moving, produces current flow. In
a semiconductor two types of charge carri-
z
p (z 1 ,z 2 ) = det I n z 1 z 2 − A 1 z 1 − A z 2 2
ers exist: electrons and holes. Electrons
n 1 n 2
X X i j carry unit negative charge and have an ef-
= a ij z z (a nn = 1)
1 2
i=0 j=0 fective mass that is determined by the shape
of the conduction band in energy-momentum
is called the 2-D characteristic polynomial of space. The effective mass of an electron in a
the 2-D Fornasini–Marchesini model semiconductor is generally significantly less
than an electron in free space. Holes have
x i+1,j+1 = A 1 x i+1,j + A 2 x i,j+1 unit positive charge. Holes have an effective
mass that is determined by the shape of the
+ B 1 u i+1,j + B 2 u i,j+1
valence band in energy-momentum space.
i, j ∈ Z + (the set of nonnegative integers) The effective mass of a hole is generally sig-
n
where x ij ∈ R is the local state vector, u ij ∈ nificantly larger than that for an electron. For
c
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