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linear system theory and designpdf电子书版本下载
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图书目录
Chapter 1 Introduction 1
1-1 The Study of Systems 1
1-2 The Scope of the Book 2
Chapter 2 Linear Spaces and Linear Operators 6
2-1 Introduction 6
2-2 Linear Spaces over a Field 7
2-3 Linear Independence, Bases, and Representations 12
Change of Basis 17
2-4 Linear Operators and Their Representations 19
Matrix Representations of a Linear Operator 21
2-5 Systems of Linear Algebraic Equations 26
2-6 Eigenvectors, Generalized Eigenvectors, and Jordan-Form Representations of a Linear Operator 33
Derivation of a Jordan-Form Representation 38
2-7 Functions of a Square Matrix 45
Polynomials of a Square Matrix 45
Functions of a Square Matrix 51
Functions of a Matrix Defined by Means of Power Series 54
2-8 Norms and Inner Product 57
2-9 Concluding Remarks 60
Problems 62
Chapter 3 Mathematical Descriptlons of Systems 70
3-1 Introduction 70
3-2 The Input-Output Description 72
Linearity 73
Causality 76
Relaxedness 77
Time Invariance 80
Transfer-Function Matrix 81
3-3 The State-Variable Description 83
The Concept of State 83
Dynamical Equations 86
Linearity 87
Time Invariance 89
Transfer-Function Matrix 90
Analog and Digital Computer Simulations of Linear Dyna-mical Equations 91
3-4 Examples 94
Dynamical Equations for RLC Networks 101
3-5 Comparisons of the Input-Output Description and the State-Variable Description 106
3-6 Mathematical Descriptions of Composite Systems 108
Time-Varying Case 108
Time-Invariant Case 111
Well-Posedness Problem 114
3-7 Discrete-Time Systems 121
3-8 Concluding Remarks 124
Problems 125
Chapter 4 Linear Dynamical Equations and Impulse-Response Matrices 133
4-1 Introduction 133
4-2 Solutions of a Dynamical Equation 134
Time-Varying Case 134
Solutions of x = A(t)x 134
Solutions of the Dynamical Equation E 139
Time-Invariant Case 141
4-3 Equivalent Dynamical Equations 146
Time-Invariant Case 146
Time-Varying Case 151
Linear Time-Varying Dynamical Equation withPeriodic A(·) 153
4-4 Impulse-Response Matrices and Dynamical Equations 154
Time-Varying Case 154
Time-Invariant Case 157
4-5 Concluding Remarks 161
Problems 162
Chapter 5 Controllability and Observability of Linear Dynamical Equatlons 168
5-1 Introduction 168
5-2 Linear Independence of Time Functions 170
5-3 Controllability of Linear Dynamical Equations 175
Time-Varying Case 175
Differential Controllability, Instantaneous Controllabil-ity, and Uniform Controllability 180
Time-Invariant Case 183
Controllability Indices 187
5-4 Observability of Linear Dynamical Equations 192
Time-Varying Case 192
Differential Observability, Instantaneous Observabil-ity, and Uniform Observability 196
Linear Time-Invariant Dynamical Equations 197
Observability Indices 198
5-5 Canonical Decomposition of a Linear Time-Invariant Dyna-mical Equation 199
Irreducible Dynamical Equations 206
5-6 Controllability and Observability of Jordan-Form Dynamical Equations 209
5-7 Output Controllability and Output Function Controllability 214
5-8 Computational Problems 217
5-9 Concluding Remarks 226
Problems 227
Chapter 6 Irreducible Realizations, Strict System Equivalence, and Identification 232
6-1 Introduction 232
6-2 The Characteristic Polynomial and the Degree of a Proper Rational Matrix 234
6-3 Irreducible Realizations of Proper Rational Functions 237
Irreducible Realization of β3/D(s) 237
Irreducible Realizations of g(s) = N(s)/D(s) 240
Observable Canonical-Form Realization 240
Controllable Canonical-Form Realization 243
Realization from the Hankel Matrix 245
Jordan-Canonical-Form Realization 249
Realization of Linear Time-Varying Differential Equations 252
6-4 Realizations of Vector Proper Rational Transfer Functions 253
Realization from the Hankel Matrix 257
6-5 Irreducible Realizations of Proper Rational Matrices: Hankel Methods 265
Method Ⅰ.Singular Value Decomposition 268
Method Ⅱ.Row Searching Method 272
6-6 Irreducible Realizations of (s): Coprime Fraction Method 276
Controllable-Form Realization 276
Realization of N(s)D-1(s), Where D(s) and N(s) Are NotRight Coprime 282
Column Degrees and Controllability Indices 284
Observable-Form Realization 285
6-7 Polynomial Matrix Description 287
6-8 Strict System Equivalence 292
6-9 Identification of Discrete-Time Systems from Noise-Free Data 300
Persistently Exciting Input Sequences 307
Nonzero Initial Conditions 309
6-10 Concluding Remarks 313
Problems 317
Chapter 7 State Feedback and State Estimators 324
7-1 Introduction 324
7-2 Canonical-Form Dynamical Equations 325
Single-Variable Case 325
Multivariable Case 325
7-3 State Feedback 334
Single-Variable Case 334
Stabilization 339
Effect on the Numerator of g(s) 339
Asymptotic Tracking Problem—Nonzero SetPoint 340
Multivariable Case 341
Method Ⅰ 341
Method Ⅱ 345
Method Ⅲ 347
Nonuniqueness of Feedback Gain Matrix 348
Assignment of Eigenvalues and Eigenvectors 351
Effect on the Numerator Matrix of G(s) 352
Computational Problems 353
7-4 State Estimators 354
Full-Dimensional State Estimator 355
Method Ⅰ 357
Method Ⅱ 358
Reduced-Dimensional State Estimator 361
Method Ⅰ 361
Method Ⅱ 363
7-5 Connection of State Feedback and State Estimator 365
Functional Estimators 369
7-6 Decoupling by State Feedback 371
7-7 Concluding Remarks 377
Problems 378
Chapter 8 Stablllty of Llnear Systems 384
8-1 Introduction 384
8-2 Stability Criteria in Terms of the Input-Output Description 385
Tine-Varying Case 385
Time-Invariant Case 388
8-3 Routh-Hurwitz Criterion 395
8-4 Stability of Linear Dynamical Equations 400
Time-Varying Case 400
Time-Invariant Case 407
8-5 Lyapunov Theorem 412
A Proof of the Routh-Hurwitz Criterion 417
8-6 Discrete-Time Systems 419
8-7 Concluding Remarks 425
Problems 425
Chapter 9 Llnear Tlme-Invarlant Composlte Systems: Characterlza-tlon, Stablllty, and Deslgns 432
9-1 Introduction 432
9-2 Complete Characterization of Single-Variable Composite Systems 434
9-3 Controllability and Observability of Composite Systems 439
Parallel Connection 440
Tandem Connection 441
Feedback Connection 444
9-4 Stability of Feedback Systems 448
Single-Variable Feedback System 449
Multivariable Feedback System 451
9-5 Design of Compensators: Unity Feedback Systems 458
Single-Variable Case 458
Single-Input or Single-Output Case 464
Multivariable Case—Arbitrary Pole Assignment 468
Multivariable Case—Arbitrary Denominator-Matrix Assignment 478
Decoupling 486
9-6 Asymptotic Tracking and Disturbance Rejection 488
Single-Variable Case 488
Multivariable Case 495
Static Decoupling—Robust and NonrobustDesigns 501
State-Variable Approach 504
9-7 Design of Compensators: Input-Output FeedbackSytems 506
Single-Variable Case 506
Multivariable Case 511
Implementations of Open-Loop Compensators 517
Implementation Ⅰ 517
Implementation Ⅱ 519
Applications 523
Decoupling 523
Asymptotic Tracking, Disturbance Rejection, andDecoupling 526
9-8 Concluding Remarks 534
Problems 536
Appendix A Elementary Transformations 542
A-1 Gaussian Elimination 543
A-2 Householder Transformation 544
A-3 Row Searching Algorithm 546
A-4 Hessenberg Form 551
Problems 553
Appendix B Analytic Functions of a Real Variable 554
Appendix C Minimum Energy Control 556
Appendix D Controllability after the Introduction of Sampling 559
Problems 564
Appendix E Hermitian Forms and Singular Value Decomposition 565
Problems 570
Appendix F On the Matrix Equation AM + MB = N 572
Problems 576
Appendix G Polynomials and Polynomial Matrices 577
G-1 Coprimeness of Polynomials 577
G-2 Reduction of Reducible Rational Functions 584
G-3 Polynomial Matrices 587
G-4 Coprimeness of Polynomial Matrices 592
G-5 Column- and Row-Reduced Polynomial Matrices 599
G-6 Coprime Fractions of Proper Rational Matrices 605
Problems 618
Appendix H Poles and Zeros 623
Problems 635
References 636
Index 657