Nonlinear Systems Third Edition2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Introduction1

1.1 Nonlinear Models and Nonlinear Phenomena1

1.2 Examples5

1.2.1 Pendulum Equation5

1.2.2 Tunnel-Diode Circuit6

1.2.3 Mass-Spring System8

1.2.4 Negative-Resistance Oscillator11

1.2.5 Artificial Neural Network14

1.2.6 Adaptive Control16

1.2.7 Common Nonlinearities18

1.3 Exercises24

2 Second-Order Systems35

2.1 Qualitative Behavior of Linear Systems37

2.2 Multiple Equilibria46

2.3 Qualitative Behavior Near Equilibrium Points51

2.4 Limit Cycles54

2.5 Numerical Construction of Phase Portraits59

2.6 Existence of Periodic Orbits61

2.7 Bifurcation69

2.8 Exercises76

3 Fundamental Properties87

3.1 Existence and Uniqueness88

3.2 Continuous Dependence on Initial Conditions and Parameters95

3.3 Differentiability of Solutions and Sensitivity Equations99

3.4 Comparison Principle102

3.5 Exercises105

4 Lyapunov Stability111

4.1 Autonomous Systems112

4.2 The Invariance Principle126

4.3 Linear Systems and Linearization133

4.4 Comparison Functions144

4.5 Nonautonomous Systems147

4.6 Linear Time-Varying Systems and Linearization156

4.7 Converse Theorems162

4.8 Boundedness and Ultimate Boundedness168

4.9 Input-to-State Stability174

4.10 Exercises181

5 Input-Output Stability195

5.1 L Stability195

5.2 L Stability of State Models201

5.3 L2 Gain209

5.4 Feedback Systems：The Small-Gain Theorem217

5.5 Exercises222

6 Passivity227

6.1 Memoryless Functions228

6.2 State Models233

6.3 Positive Real Transfer Functions237

6.4 L2 and Lyapunov Stability241

6.5 Feedback Systems：Passivity Theorems245

6.6 Exercises259

7 Frequency Domain Analysis of Feedback Systems263

7.1 Absolute Stability264

7.1.1 Circle Criterion265

7.1.2 Popov Criterion275

7.2 The Describing Function Method280

7.3 Exercises296

8 Advanced Stability Analysis303

8.1 The Center Manifold Theorem303

8.2 Region of Attraction312

8.3 Invariance-like Theorems322

8.4 Stability of Periodic Solutions329

8.5 Exercises334

9 Stability of Perturbed Systems339

9.1 Vanishing Perturbation340

9.2 Nonvanishing Perturbation346

9.3 Comparison Method350

9.4 Continuity of Solutions on the Infinite Interval355

9.5 Interconnected Systems358

9.6 Slowly Varying Systems365

9.7 Exercises372

10 Perturbation Theory and Averaging381

10.1 The Perturbation Method382

10.2 Perturbation on the Infinite Interval393

10.3 Periodic Perturbation of Autonomous Systems397

10.4 Averaging402

10.5 Weakly Nonlinear Second-Order Oscillators411

10.6 General Averaging413

10.7 Exercises419

11 Singular Perturbations423

11.1 The Standard Singular Perturbation Model424

11.2 Time-Scale Properties of the Standard Model430

11.3 Singular Perturbation on the Infinite Interval439

11.4 Slow and Fast Manifolds443

11.5 Stability Analysis449

11.6 Exercises460

12 Feedback Control469

12.1 Control Problems469

12.2 Stabilization via Linearization475

12.3 Integral Control478

12.4 Integral Control via Linearization481

12.5 Gain Scheduling485

12.6 Exercises499

13 Feedback Linearization505

13.1 Motivation505

13.2 Input-Output Linearization509

13.3 Full-State Linearization521

13.4 State Feedback Control530

13.4.1 Stabilization530

13.4.2 Tracking540

13.5 Exercises544

14 Nonlinear Design Tools551

14.1 Sliding Mode Control552

14.1.1 Motivating Example552

14.1.2 Stabilization563

14.1.3 Tracking572

14.1.4 Regulation via Integral Control575

14.2 Lyapunov Redesign579

14.2.1 Stabilization579

14.2.2 Nonlinear Damping588

14.3 Backstepping589

14.4 Passivity-Based Control604

14.5 High-Gain Observers610

14.5.1 Motivating Example612

14.5.2 Stabilization619

14.5.3 Regulation via Integral Control623

14.6 Exercises625

A Mathematical Review647

B Contraction Mapping653

C Proofs657

C.1 Proof of Theorems 3.1 and 3.2657

C.2 Proof of Lemma 3.4659

C.3 Proof of Lemma 4.1661

C.4 Proof of Lemma 4.3662

C.5 Proof of Lemma 4.4662

C.6 Proof of Lemma 4.5663

C.7 Proof of Theorem 4.16665

C.8 Proof of Theorem 4.17669

C.9 Proof of Theorem 4.18675

C.10 Proof of Theorem 5.4676

C.11 Proof of Lemma 6.1677

C.12 Proof of Lemma 6.2680

C.13 Proof of Lemma 7.1684

C.14 Proof of Theorem 7.4688

C.15 Proof of Theorems 8.1 and 8.3690

C.16 Proof of Lemma 8.1699

C.17 Proof of Theorem 11.1700

C.18 Proof of Theorem 11.2706

C.19 Proof of Theorem 12.1708

C.20 Proof of Theorem 12.2709

C.21 Proof of Theorem 13.1710

C.22 Proof of Theorem 13.2712

C.23 Proof of Theorem 14.6713

Note and References719

Bibliography724

Symbols740

Index742