威尔逊·Rugh线性系统理论第二版高清资源

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Rugh的《线性系统理论》第二版是一本由Johns Hopkins University电气与计算机工程系的J.R. Wilson教授撰写的经典教材。本书是Prentice Hall出版的信息与系统科学系列之一，提供了深入浅出的控制理论和线性系统分析的基础知识。第二版更新了内容，包含了最新的研究成果和技术发展，适合于工程师、科研人员以及高级学生学习和参考。该书的主要内容涵盖了线性系统的基本概念，如系统的数学模型、稳定性分析、动态行为、频率响应、控制系统设计和数字信号处理等核心主题。读者可以从中了解到如何运用线性系统理论解决实际问题，如自动控制、通信系统和信号处理中的挑战。书中不仅提供了理论阐述，还配以丰富的实例和习题，帮助读者通过实践加深理解。此外，作者在书中引用了大量的文献资料和参考资料，为深入研究者提供了进一步探索的途径。为了方便查找，书籍还附有详细的索引，使得查找特定主题变得简单快捷。《线性系统理论》第二版不仅适用于课堂教学，也是独立学习者的宝贵资源。它遵循严谨的学术标准，同时注重实用性和可操作性，使读者能够在理论与实践中找到平衡，提升在信息技术领域的专业素养。在版权方面，本书享有1996年Prentice-Hall, Inc.的版权保护，未经许可，不得任何形式复制或传播。这是一部经过精心编排和审校的专业著作，旨在推动线性系统理论的发展和应用。 Rugh的《线性系统理论》第二版是每个寻求深入了解线性系统理论及其在现代信息技术领域应用的学者和工程师的理想参考书，是系统学习和实践不可或缺的工具。

MATHEMATICAL

NOTATION

AND

REVIEW

Throughout this book

we use

mathematical analysis, linear algebra,

and

matrix theory

what

might

called

advanced undergraduate level.

For

some

topics

review might

beneficial

to the

typical

reader,

and the

best sources

for

such review

are

mathematics

texts.

Here

quick listing

basic

notions

provided

to set

notation

and

provide

reminders.

addition there

are

exercises

that

can be

solved

reasonably

straightforward applications

these notions. Results

exercises

this chapter

are

used

in the

sequel,

and

therefore

the

exercises

should

perused,

least.

With

minor

exceptions

all the

mathematical tools

Chapters 2-15,

20-29

are

self-contained

developments

material reviewed

here.

Chapters

16-19 additional mathematical

background

introduced

for

local

purposes.

Basic mathematical objects

linear system theory

are

x 1 or 1 x

vectors

and

matrices

with

real entries, though

occasion complex entries

arise.

Typically

vectors

are in

lower-case italics, matrices

are in

upper-case italics,

and

scalars (real,

sometimes complex)

are

represented

Greek letters. Usually

the

/'''-entry

in a

vector

denoted

A-,-,

and the

/,./-entry

matrix

A is

written

a-tj

[A]y.

These

notations

are

not

completely consistent,

if for no

other reason than scalars

can be

viewed

special

cases

vectors,

and

vectors

can be

viewed

special

cases

matrices.

Moreover,

notational conventions

are

abandoned when they collide with strong tradition.

With

the

usual

definition

addition

and

scalar

multiplication,

the set of

all

x 1

vectors and,

generally,

the set of all m x n

matrices,

can be

viewed

vector

spaces

over

the

real

(or

complex)

field. In the

real

case

the

vector

space

;;

x 1

vectors

written

or s

imply

R",

and a

vector

space

matrices

written

R"'x

The

default

throughout

is the

real

case—when

matrices

vectors

with

complex entries

V-l

) are at

issue, special mention

will

made.

It is

useful

for

some

of the

later

chapters

review

the

axioms

for a field and a

vector

space,

though

for

most

of the

book

technical

developments

are

phrased

in the

language

matrix

algebra.

Matrices

Overbar

denotes

the

complex conjugate,

when transpose

is not

desired.

For

scalar

either

correctly construed

complex conjugate,

and

is the

magnitude

of x.

Matrices

For

matrices there

are

several standard concepts

and

special

notations used

in the

sequel.

The

matrix

with

all

entries zero

written

x,,,

simply

when dimensional

emphasis

is not

needed.

For

square matrices,

m = n, the

zero

matrix sometimes

written

0,,,

while

the

identity matrix

written similarly

/„

or /. We

reserve

the

notation

for the

^'''-column

£'''-row,

depending

context,

of the

identity matrix.

The

notions

addition

and

multiplication

for

conformable matrices

are

presumed

to be

familiar.

course

the

multiplication operation

more interesting,

part because

is not

commutative

general.

That

is,

and

are not

always

the

same.

If A is

square, then

for

nonnegative integer

the

power

well defined,

with

A°

= I. If

there

positive

such that

= 0,

then

A is

called

nilpotent.

Similar

to the

vector case,

the

transpose

of a

matrix

with entries

atj

is the

matrix

with

/J-entry

given

a,-,-.

useful

fact

(AB)T

BTAT.

For a

square

x n

matrix

A, the

trace

is the sum of the

diagonal entries, written

trA

i>,.

(4)

i=l

also

is n x

then

//•

[AB]

[BA].

familiar scalar-valued function

of a

square matrix

A is the

determinant.

The

determinant

of A can be

evaluated

via the

Laplace expansion described

follows.

Let

Cjj

denote

the

cofactor

corresponding

to the

entry

a-,j.

Recall that

c//

1)'+J

times

the

determinant

of the

(H-l)x(«-I)

matrix that results when

the

/'''-row

and

j'1'-

column

of A are

deleted.

Then

for any fixed

<n,

det

A =

a^y

/-i

This

is the

expansion

of the

determinant along

the

/'''-row.

similar formula holds

for

the

expansion along

column. Aside

from

being

useful

representation

for the

determinant, recursive

use of

this expression provides

method

for

computing

the

determinant

of a

matrix from

the

fact

that

the

determinant

of a

scalar

simply

the

scalar

itself. Since this procedure expresses

the

determinant

as a sum of

products

entries

the

matrix,

the

determinant viewed

as a

function

of the

matrix entries

continuously

differentiable

any

number

times. Finally

if B

also

is n X n,

then

det

(AB)

det

A • det B = det

(BA)

(5)

The

matrix

A has an

inverse, written

~',

if and

only

if det A

0. One

formula

for

A"1

that occurs

often

based

on the

cofactors

of A. The

adjugate

of A,

written

adj

A, is the

matrix with

/j-entry

given

by the

cofactor

cj7.

other words,

adj

A is the

transpose

of the

matrix

cofactors. Then

Chapter

Mathematical

Notation

and

Review

adj A

det

standard, collapsed

way of

writing

the

product

of the

scalar

\l(det

A) and the

matrix

adj

A. The

inverse

of a

product

square, invertible matrices

given

=B-[A

A is

X n and p is a

nonzero

n x 1

vector such that

for

some scalar

Ap =

"kp

(6)

then

p is an

eigenvector corresponding

to the

eigenvalue

course

must

presumed nonzero,

for if p = 0,

then this equation

satisfied

for any X.

Also

any

nonzero scalar multiple

of an

eigenvector

another eigenvector.

must

be a bit

careful

here, because

real matrix

can

have complex eigenvalues

and

eigenvectors,

though

the

eigenvalues must occur

conjugate pairs,

and

conjugate corresponding

eigenvectors

can be

assumed.

other words

if Ap

=•

Xp,

then

A p

="kp.

These

notions

can

refined

viewing

(6) as the

definition

of a

right

eigenvector-.

Then

it is

natural

define

left

eigenvector

for A as a

nonzero

1 x n

vector

such that

qA =

"kq

for

some

eigenvalue

The n

eigenvalues

of A are

precisely

the n

roots

of the

characteristic polynomial

given

by del

(si,,

-A).

Since

the

roots

of a

polynomial

are

continuous

functions

the

coefficients

of the

polynomial,

the

eigenvalues

of a

matrix

are

continuous functions

the

matrix entries. Recall that

the

product

of the n

eigenvalues

of A

gives

det A,

while

the sum of the n

eigenvalues

The

Cayley-Hamilton

theorem states that

then

det

(si,,

•

• • +

]A"

+ • • • +

ajA

a0In

=0,,

Our

main application

this result

is to

write

A"+k,

for

integer

£>0,

as a

linear

combination

of /,

A"~'.

similarity transformation

of the

type

T~]AT,

where

A and

invertible

T are

xn,

occurs frequently.

It is a

simple exercise

show that

T~1AT

and A

have

the

same

set of

eigenvalues.

If A has

distinct

eigenvalues,

and T has as

columns

corresponding

set of

(linearly independent) eigenvectors

for A,

then

T~[AT

is a

diagonal matrix, with

the

eigenvalues

of A as the

diagonal entries. Therefore

this

computation

can

lead

to a

matrix with complex entries.

1.1

Example

The

characteristic polynomial

-2

(7)

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威尔逊·Rugh线性系统理论第二版高清资源

linear system theory and design 文字版 第三版 有目录

Linear System Theory and Design(单页版)

WILSON J. RUGH 线性系统理论课后习题答案

在项目实战中，如何运用Volterra/Wiener方法对非线性系统进行输入/输出特性分析，并举例说明如何构建Volterra级数模型？

如何利用Volterra/Wiener方法分析非线性系统的输入/输出特性？

在面对复杂非线性系统时，如何应用Volterra/Wiener方法进行系统特性分析和建模？请结合实际案例详细解释。

LinearSystemTheory_Design 答案

Linear Systems Theory

Rugh W.J. linear_System_Theory_(2ed.__PH_1995)(ISBN_0134412052)(T)

【含数据库+附源码+说明文档】基于Java swing和mysql实现的银行管理系统（彩色版本）

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linear system theory and design 文字版第三版有目录