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Rational function systems and electrical networks with multiparameters
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Description
Rating
Title
Rational
function
systems
and
electrical
networks
with
multiparameters
Creator
Lu, KaiSheng
Contributors
World Scientific (Firm)
DescriptionAbstract
To
overcome
the
problems
of
system
theory
and
network
theory
over
real
field
, this
book
uses
matrices
over
the
field
F(z)
of
rational
functions
in
multiparameters
describing
coefficient
matrices
of
systems
and
networks
and
makes
systems
and
network
description
over
F(z)
and
researches
their
structural
properties
:
reducible
condition
of a
class
of
matrices
over
F(z)
and their
characteristic
polynomial
;
type1
matrix
and
two
basic
properties
;
variable
replacement
conditions
for
independent
parameters
;
structural
controllability
and
observability
of
linear
systems
over
F(z)
;
separability
,
reducibility
,
controllability
,
observability
and
structural
conditions
of
networks
over
F(z)
, and
so
on. This
book
involves
three
subjects
:
systems
,
networks
and
matrices
over
F(z)
,
which
is
an
achievement
of
interdisciplinary
research
.
DescriptionTable Of Contents
1
.
Introduction

2
.
Matrices
over
field
F(z)
of
rational
functions
in
multiparameters
.
2.1
.
Polynomials
over
field
F(z)
or
ring
F(z)[λ]
.
2.2
.
Operations
and
determinant
of
matrix
over
F(z)
.
2.3
.
Elementary
operations
of
matrices
over
F(z)
and
some
conclusions
.
2.4
.
Operation
and
canonical
form
of
matrix
over
F(z)
.
2.5
.
Reducibility
of
square
matrix
over
F(z)
.
2.6
.
Reducibility
condition
of
class
of
matrices
over
F(z)
.
2.7
.
Two
properties
.
2.8
.
Independent
parameters
and a
class
of
irreducible
polynomials
over
F(z)[λ]
.
2.9
.
Conclusions
.
2.10
.
New
model
and its
reducibility

3
.
Controllability
and
observability
of
linear
systems
over
F(z)
.
3.1
.
Controllability
and
observability
in
time
domain
.
3.2
.
Controllability
and
observability
in
frequency
domain

4
.
Electrical
networks
over
F(z)
.
4.1
.
Resistorsource
networks
over
F(z)
.
4.2
.
Separability
and
reducibility
conditions
of
RLC
networks
over
F(z)
and their
applications
.
4.3
.
Controllability
and
observability
of
RLC
networks
over
F(z)
.
4.4
.
Structural
condition
of
controllability
for
RLC
networks
over
F(z)
.
4.5
.
Structural
condition
of
observability
for
RLC
networks
over
F(z)
.
4.6
.
Separability
,
reducibility
,
controllability
and
observability
of
RLCM
networks
over
F(z)
.
4.7
.
Existence
of
state
equations
of
linear
active
networks
over
F(z)
.
4.8
. A
sufficient
condition
on
controllability
and
observability
of
active
networks
over
F(z)
.
4.9
.
Conditions
on
[symbol]
of
active
network
over
F(z)
and
reducibility
condition
of
[symbol]
and their
applications
to
controllability
and
observability
.
4.10
.
Computer
assistant
analysis
program
for
networks
over
F(z)

5
.
Further
thought
.
5.1
.
Independent
parameters

the
third
type
of
variables
of
systems
.
5.2
.
Physical
realization
.
5.3
.
Some
issues
.
5.4
.
Quasi
structural
controllability
and
observability
concept
of
nonlinear
systems
and its
applications
.
Publisher
Higher Education Press
World Scientific Pub. Co.
Subject
Electric circuits  Mathematics.
Matrices.
Identifier
9789814412438
(electronic
bk.)
;
9789814412421
;
http://www.worldscientific.com/worldscibooks/10.1142/8524#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xiii, 304 p. : ill.
Date
c2012
.
OCLC number
874502253
CONTENTdm number
530
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