目錄
第1章 線性系統(tǒng)的數(shù)學(xué)描述 1
1.1 基本概念 1
1.1.1 因果性 2
1.1.2 線性 3
1.1.3 時(shí)不變性 3
1.2 系統(tǒng)的輸入-輸出描述 4
1.2.1 線性系統(tǒng)的脈沖響應(yīng) 5
1.2.2 線性定常系統(tǒng)的傳遞函數(shù)矩陣 7
1.2.3 傳遞函數(shù)矩陣的 Smith-McMillan 形 8
1.2.4 傳遞函數(shù)矩陣的極點(diǎn)和零點(diǎn) 13
1.3 線性系統(tǒng)的狀態(tài)空間描述 14
1.3.1 線性系統(tǒng)的動(dòng)態(tài)方程 14
1.3.2 線性定常系統(tǒng)的特征結(jié)構(gòu) 17
1.3.3 根據(jù)狀態(tài)空間描述求傳遞函數(shù)矩陣 18
1.3.4 動(dòng)態(tài)系統(tǒng)的等價(jià) 22
第2章 線性系統(tǒng)的動(dòng)態(tài)響應(yīng) 31
2.1 概述 31
2.2 線性時(shí)變系統(tǒng)的動(dòng)態(tài)響應(yīng) 32
2.2.1 線性時(shí)變系統(tǒng)的狀態(tài)轉(zhuǎn)移矩陣 33
2.2.2 線性時(shí)變系統(tǒng)的零輸入響應(yīng) 37
2.2.3 線性時(shí)變系統(tǒng)的零狀態(tài)響應(yīng) 38
2.2.4 線性時(shí)變系統(tǒng)的狀態(tài)響應(yīng)和輸出響應(yīng) 39
2.3 線性定常系統(tǒng)的動(dòng)態(tài)響應(yīng) 41
2.3.1 線性定常系統(tǒng)的矩陣指數(shù).41
2.3.2 線性定常系統(tǒng)的零輸入響應(yīng) 48
2.3.3 線性定常系統(tǒng)的零狀態(tài)響應(yīng) 50
2.3.4 線性定常系統(tǒng)的狀態(tài)響應(yīng)和輸出響應(yīng) 51
第3章 線性系統(tǒng)的能控性和能觀性 54
3.1 線性系統(tǒng)的能控性 54
3.1.1 基本概念 54
3.1.2 線性時(shí)變系統(tǒng)的能控性判據(jù) 56
3.1.3 線性定常系統(tǒng)的能控性判據(jù) 60
3.1.4 線性定常系統(tǒng)的能控性指數(shù) 66
3.2 線性系統(tǒng)的能觀性 69
3.2.1 基本概念 69
3.2.2 線性時(shí)變系統(tǒng)的能觀性判據(jù) 71
3.2.3 線性定常系統(tǒng)的能觀性判據(jù) 73
3.2.4 線性定常系統(tǒng)的能觀性指數(shù) 76
3.3 線性系統(tǒng)的對(duì)偶原理 78
3.3.1 對(duì)偶系統(tǒng) 78
3.3.2 對(duì)偶原理 79
3.4 線性定常系統(tǒng)的結(jié)構(gòu)分解 80
3.4.1 線性系統(tǒng)在等價(jià)變換下的能控性和能觀性 81
3.4.2 線性定常系統(tǒng)的能控性結(jié)構(gòu)分解 81
3.4.3 線性定常系統(tǒng)的能觀性結(jié)構(gòu)分解 85
3.4.4 線性定常系統(tǒng)的 Kalman分解 86
3.4.5 極點(diǎn)、零點(diǎn)和特征值間的關(guān)系 89
第4章 線性定常系統(tǒng)的標(biāo)準(zhǔn)形和實(shí)現(xiàn) 94
4.1 線性定常系統(tǒng)的標(biāo)準(zhǔn)形 94
4.1.1 線性定常 SISO系統(tǒng)的標(biāo)準(zhǔn)形 94
4.1.2 線性定常 MIMO系統(tǒng)的標(biāo)準(zhǔn)形 99
4.2 能控性和能觀性的頻域形式 107
4.3 線性定常系統(tǒng)的實(shí)現(xiàn) 108
4.3.1 基本概念 108
4.3.2 線性定常SISO系統(tǒng)的實(shí)現(xiàn) 109
4.3.3 線性定常MIMO系統(tǒng)的實(shí)現(xiàn) 111
4.4 線性定常系統(tǒng)的最小實(shí)現(xiàn) 114
4.4.1 基本概念 114
4.4.2 線性定常SISO系統(tǒng)的最小實(shí)現(xiàn) 118
4.4.3 線性定常MIMO系統(tǒng)的最小實(shí)現(xiàn) 121
第5章 線性系統(tǒng)的穩(wěn)定性 125
5.1 Lyapunov穩(wěn)定理論 125
5.1.1 基本概念 125
5.1.2 Lyapunov第二法的主要定理 129
5.2 線性系統(tǒng)的內(nèi)部穩(wěn)定性.134
5.2.1 線性時(shí)變系統(tǒng)的內(nèi)部穩(wěn)定性.134
5.2.2 線性定常系統(tǒng)的內(nèi)部穩(wěn)定性.138
5.3 線性系統(tǒng)的外部穩(wěn)定性.142
5.3.1 線性系統(tǒng)的 BIBO 穩(wěn)定性 142
5.3.2 線性系統(tǒng)的 BIBS 穩(wěn)定性 144
5.4 外部穩(wěn)定和內(nèi)部穩(wěn)定的關(guān)系 145
第6章 線性系統(tǒng)的時(shí)域綜合與反饋控制 148
6.1 狀態(tài)反饋控制 148
6.1.1 狀態(tài)反饋系統(tǒng)的能控性和能觀性 148
6.1.2 SISO系統(tǒng)的狀態(tài)反饋特征值配置 150
6.1.3 MIMO系統(tǒng)的狀態(tài)反饋特征值配置 154
6.1.4 狀態(tài)反饋鎮(zhèn)定 162
6.2 輸出反饋控制 166
6.2.1 輸出反饋系統(tǒng)的能控性和能觀性 166
6.2.2 輸出反饋特征值配置 167
6.2.3 動(dòng)態(tài)輸出反饋補(bǔ)償器 174
6.3 解耦控制 177
6.3.1 基本概念 177
6.3.2 狀態(tài)反饋解耦 180
6.3.3 穩(wěn)態(tài)解耦 186
6.4 狀態(tài)觀測(cè)器 188
6.4.1 全維狀態(tài)觀測(cè)器 188
6.4.2 降維狀態(tài)觀測(cè)器 191
6.4.3 函數(shù)狀態(tài)觀測(cè)器 195
6.4.4 帶狀態(tài)觀測(cè)器的動(dòng)態(tài)系統(tǒng) 198
參考文獻(xiàn) 203
Contents
Chapter 1 Mathematical Description of Linear Systems 205
1.1 Basic Concepts 205
1.1.1 Causality 206
1.1.2 Linearity 207
1.1.3 Time-Invariance 208
1.2 Input-Output Description of Linear Systems 209
1.2.1 Impulse Response of Linear Systems 209
1.2.2 Transfer Function Matrix of Linear Time-Invariant Systems.212
1.2.3 Smith-McMillan Form of Transfer Function Matrices 213
1.2.4 Poles and Zeros of Transfer Function Matrices 218
1.3 State Space Description of Linear Systems 219
1.3.1 Dynamical Equations of Linear Systems 220
1.3.2 Characteristic Structures of Linear Time-Invariant Systems 223
1.3.3 Deriving Transfer Function Matrix from State Space Description 224
1.3.4 Equivalence of Dynamical Systems 228
Assignments 236
Chapter 2 Response of Linear Dynamical Systems 238
2.1 Introduction 238
2.2 Response of Linear Time-Varying Dynamical Systems 240
2.2.1 State Transition Matrix of Linear Time-Varying Systems 240
2.2.2 Zero-Input Response of Linear Time-Varying Systems 245
2.2.3 Zero-State Response of Linear Time-Varying Systems 246
2.2.4 State Response and Output Response of Linear Time-Varying Systems 247
2.3 Response of Linear Time-Invariant Dynamical Systems.249
2.3.1 Matrix Exponential of Linear Time-Invariant Systems.250
2.3.2 Zero-Input Response of Linear Time-Invariant Systems 257
2.3.3 Zero-State Response of Linear Time-Invariant Systems 259
2.3.4 State Response and Output Response of Linear Time-Invariant Systems 260
Assignments 261
Chapter 3 Controllability and Observability of Linear Systems 264
3.1 Controllability of Linear Systems 264
3.1.1 Basic Concepts.264
3.1.2 Controllability Criteria of Linear Time-Varying Systems 267
3.1.3 Controllability Criteria of Linear Time-Invariant Systems 270
3.1.4 Controllability Index of Linear Time-Invariant Systems.277
3.2 Observability of Linear Systems.279
3.2.1 Basic Concepts.279
3.2.2 Observability Criteria of Linear Time-Varying Systems 282
3.2.3 Observability Criteria of Linear Time-Invariant Systems 284
3.2.4 Observability Index of Linear Time-Invariant Systems 287
3.3 Duality Principle of Linear Systems 289
3.3.1 Dual Systems 290
3.3.2 Duality Principle 291
3.4 Structure Decomposition of Linear Time-Invariant Systems 292
3.4.1 Controllability and Observability of Linear Systems with Equivalent Transformation 292
3.4.2 Controllability Structure Decomposition of Linear Time-Invariant Systems.293
3.4.3 Observability Structure Decomposition of Linear Time-Invariant Systems 296
3.4.4 Kalman’s Decomposition of Linear Time-Invariant Systems 298
3.4.5 Relationships among Poles, Zeros and Eigenvalues 301
Assignments 305
Chapter 4 Canonical Form and Realization of Linear Time-Invariant Systems 308
4.1 Canonical Form of Linear Time-Invariant Systems 308
4.1.1 Canonical Form of Linear Time-Invariant SISO Systems 308
4.1.2 Canonical Form of Linear Time-Invariant MIMO Systems 313
4.2 Controllability and Observability in Frequency Domain 321
4.3 Realization of Linear Time-Invariant Systems 323
4.3.1 Basic Concepts 323
4.3.2 Realization of Linear Time-Invariant SISO Systems 324
4.3.3 Realization of Linear Time-Invariant MIMO Systems 326
4.4 Minimal Realization of Linear Time-Invariant Systems 329
4.4.1 Basic Concepts 329
4.4.2 Minimal Realization of Linear Time-Invariant SISO Systems 334
4.4.3 Minimal Realization of Linear Time-Invariant MIMO Systems 337
Assignments 340
Chapter 5 Stability of Linear Systems 342
5.1 Lyapunov Stability Theory 342
5.1.1 Basic Concepts.342
5.1.2 Main Theorems of Lyapunov’s Second Method 346
5.2 Internal Stability of Linear Systems 351
5.2.1 Internal Stability of Linear Time-Varying Systems 352
5.2.2 Internal Stability of Linear Time-Invariant Systems 356
5.3 External Stability of Linear Systems 360
5.3.1 BIBO Stability of Linear Systems 361
5.3.2 BIBS Stability of Linear Systems 363
5.4 Relationships between External Stability and Internal Stability 364
Assignments 366
Chapter 6 Synthesis and Feedback Control of Linear Systems in Time Domain 369
6.1 State Feedback Control 369
6.1.1 Controllability and Observability of System with State Feedback 369
6.1.2 Eigenvalue Assignment with State Feedback for SISO Systems 371
6.1.3 Eigenvalue Assignment with State Feedback for MIMO Systems 375
6.1.4 Stabilization with State Feedback 384
6.2 Output Feedback Control 388
6.2.1 Controllability and Observability of System with Output Feedback 388
6.2.2 Eigenvalue Assignment with Output Feedback 389
6.2.3 Dynamic Output Feedback Compensator 396
6.3 Decoupling Control 399
6.3.1 Basic Concepts.399
6.3.2 Decoupling with State Feedback 403
6.3.3 Steady State Decoupling 408
6.4 State Observer.410
6.4.1 Full-Order State Observer 410
6.4.2 Reduced-Order State Observer 414
6.4.3 Functional State Observer 418
6.4.4 Dynamical Systems with State Observer Feedback 421
Assignments 425