线性系统 Linear Systems T.Kailath 高清.pdf版
A self-contained, highly motivated and comprehensive account of basic methods for analysis and application of linear systems that arise in signal processing problems in communications, control, system identification and digital filtering.LINEAR SYSTHNIE
THOMAS KAILATH
Department of Electrical Engineering
Stanford University
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PRENTICE-HALL, INC,, Englewood Cliffs, N.J. 07632
Library of Congress Cataloging in Publication Data
af systems.
Includes bibliographies and index.
QA402K29598000379-14928
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PREFACE
XI[I
CHAPTER 1 BACKGROUND MATERIAL
I I Some Subtleties in the Definition of linearity,
1.2 Unilateral Laplace Transforms and a generalized
1.3 Impulsive Functions, Signal Representations,
and Input-Output Relations, I4
1.4 Some remarks on the Use of matrices, 27
CHAPTER 2 STATE-SPACE DESCRIPTIONS-SOME
BASIC CONCEPTS
20
al realizations. 35
2.1.I Some remarks on analog computers, 35
2.1 2 Four canonical realizations, 37
2.1.3 Parallel and cascade realizations, 45
Sections so marked throughout Contents may be skipped
Yll
2.2 State Equations in the Time and fre
22. i Matrix notation and state space equations, 50
22.2 obtuinii
乎 lions directy--s0me
examples, linearization, 55
2. 2.3 A definition of state, 62
a2.4 More names and definitions,66
2.3 Initial Conditions for Analog-Computer simulation
Observability and Controllability for Continuous
and discrete- Time realizations , 79
2.3I Determining the initial conditions,szare
23. 2 Setting up initial conditions, state controllability, &4
23.3D
bility, 90
23.4S
2. 4 Further Aspects of Controllability and obs
ty,20
2.4I Joins observability and controlability, the uses
diagonal forms, 120
2 Standard forms for noncontrollable andor
nonobservable sy stems, 728
2.4.3 The PapoyBelevirch-Hautus tests for
controllability and observability, 13.5
R2.4.4 Some tests for relatively prime polynomials, 140
2. 4,5 Some worked exan
*2.5 Solutions of state Equations and modal
Decompositions, 160
2.5.1 Time-invariant equations and matrix
exponentials, 162
2.5.2 Modes of oscillation and modal decompositions, 168
2.6 A Glimpse of Stability Thcory, 17
2, 6.2 The Lyapunov criterion, I77
26.1E
l stability
75
2.5.3 A stability resuit for linearised systems, 180
CHAPTER 3 LINEAR STATE-VARIABLE FEEDBACK
3.0 Introduction, 187
3.1 Analysis of Stabilization by Output Feedback 188
3. 2 State-Variable Feedback and Modal Controllability, 797
3. 2. Some formulas for the
3.2.2 A transfer function approach, 202
3 Some aspects of state-yariable feedback, 204
3, 3 Some worked Examples, 209
4 Quadratic Regulator Theory for ContinuousTime
Systems, 218
3.4,7O
ite solut
29
*3.4.2 Plausibility of the selection rule for the optima
*3.4.3 The algebraic Riccati equation, 230
3.5 Discrcto-Time Systems, 2
3.5.1 Modal controlability, 238
3.5.2 Controllability to the origin, state-pariable
e principle of optimality, 239
*3.5.3 The diserele-lime quadratic regulator problem, 243
*3.5.4 Square-root and related algorithms, 245
CHAPTER 4 ASYMPTOTIC OBSERVERS AND
COMPENSATOR DESIGN
259
4.0 Introduction, 259
4.1 Asymptotic Observers for State Measurcment, 250
4.2 Combined Obscrvcr-Controllcr Compensators, 268
4.3 Rcduced-order observers 281
4.4 An Optimality Critcrion for Choosing Observer Poles, 293
4.5 Direct Transfer Function Design Procedures, 297
4.5,I A transfer function reformulation of the
zer design, 298
4.5.2 Some variants of the observer-controller design, 304
4.5.3 Design via polynomial equationf, 306
CHAPTER 5 SOME ALGEBRAIC COMPLEMENTS
314
5.0 Introduction. 314
5.1 Abstract Approach to State -space Realization
Methods; Nerode Equivalence, 315
5.1.1 Realis
cov parame
5.2 Geometric Interpretation of Similarity Transformations
Linear vector Spaces, 329
5.2. Vectors in n-space: linear independence, 330
5.2.2 Matrices and transformations, 333
5.2.3 Vector subspaces, 338
5.2 4 Abstract linear vector spaces, 341
CHAPTER 6 STATE-SPACE AND MATRIX-FRACTION
DESCRIPTIONS OF MULTIVARIABLE
SYSTEM
345
6.0 Introd
61 Some Direct realizations of multivarable transfer
6.2 State Observability and Controllability
Matrix-Frection Descriptions, 352
62. The observability and controllability matrices, 35
6.2.2 Standard forms for noncontrollable nonobservable
Ins minimal realizations. 360
6. 2. 3 Mairixfrcction description, 367
6.3 Some pr
6.3.2 Unimodular matrices, the Hermite form and
coprime polynomial matrices, 373
632
d some
application, 382
63.3 The Smith form and related results, 390
rix pencils, and Kronecker form, 393
6.4 Some Basic Sta: e-Space Realizations, 403
64.i
form realizations from right MFDs, 403
iler fo
lization 408
6.4.5 Observer form realizations from left MFDs, 413
6.4.4 Controllability- and observability form realizations, 4.17
6.4.5 Canonical state-space realizations and canonical
6.4.6 Transformations of state-space realizations, 424
6.5 Some Properties of Rational Matrices, 439
6.5.1 Irreducible MFDs and minimai realizations, 439
6.5.2 The Smith-McMillan form ofH(s), 443
6.5.3 Poles and zeros of multivariable transfer functions, 446
6.5.4 Nullspace structure, minimal polynomial bases
and Kronecker indices, 455
*6.6 Ncode eg
ble Systems, 470
6.7 Canonical Matrix-Fraction and State-space
6.7.1 Hermite-form MFDs and scheme I siaie-space
67,2Pc
nialechelon mFd
Scheme i realizations, 48.7
*6.7.3 The formal definition of canonical form, 492
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