Nonlinear Systems 3rd Edition by H. Khalil
Download Nonlinear Systems 3rd Edition by H. Khalil at High Speed
This is a best-selling book, it is written in such a way that the level of mathematical sophistication builds up from chapter to chapter.
It has been reorganized into four parts: basic analysis, analysis of feedback systems, advanced analysis, and nonlinear feedback control.
Updated content includes subjects which have proven useful in nonlinear control design in recent years—new in the 3rd edition
are: expanded treatment of passivity and passivity-based control; integral control, high-gain feedback, recursive methods, optimal stabilizing control,
control Lyapunov functions, and observers. For use as a self-study or reference guide by engineers and applied mathematicians.
* Hardcover: 750 pages
* Publisher: Prentice Hall; 3 edition (December 28, 2001)
* Language: English
* ISBN-10: 0130673897
* ISBN-13: 978-0130673893
* Product Dimensions: 9.3 x 7.1 x 1.3 inches
* Shipping Weight: 2.5 pounds
* Size : 54520 KB
* Format : PDF
Contents
Preface xiii
1 Introduction 1
1.1 Nonlinear Models and Nonlinear Phenomena ............... 1
1.2 Examples .................................. 5
1.2.1 Pendulum Equation ........................ 5
1.2.2 Tunnel-Diode Circuit ....................... 6
1.2.3 Mass–Spring System ....................... 8
1.2.4 Negative-Resistance Oscillator .................. 11
1.2.5 Artificial Neural Network ..................... 14
1.2.6 Adaptive Control ......................... 16
1.2.7 Common Nonlinearities ...................... 18
1.3 Exercises .................................. 24
2 Second-Order Systems 35
2.1 Qualitative Behavior of Linear Systems .................. 37
2.2 Multiple Equilibria ............................. 46
2.3 Qualitative Behavior Near Equilibrium Points .............. 51
2.4 Limit Cycles ................................ 54
2.5 Numerical Construction of Phase Portraits ................ 59
2.6 Existence of Periodic Orbits ........................ 61
2.7 Bifurcation ................................. 69
2.8 Exercises .................................. 76
3 Fundamental Properties 87
3.1 Existence and Uniqueness ......................... 88
3.2 Continuous Dependence on Initial Conditions and Parameters ............ 95
3.3 Differentiability of Solutions and Sensitivity Equations ............ 99
3.4 Comparison Principle ........................... 102
3.5 Exercises .................................. 105
4 Lyapunov Stability 111
4.1 Autonomous Systems ........................... 112
4.2 The Invariance Principle .......................... 126
4.3 Linear Systems and Linearization ..................... 133
4.4 Comparison Functions ........................... 144
4.5 Nonautonomous Systems ......................... 147
4.6 Linear Time-Varying Systems and Linearization ............. 156
4.7 Converse Theorems ............................ 162
4.8 Boundedness and Ultimate Boundedness ................. 168
4.9 Input-to-State Stability .......................... 174
4.10 Exercises .................................. 181
5 Input–Output Stability 195
5.1 L Stability ................................. 195
5.2 L Stability of State Models ........................ 201
5.3 L 2 Gain .................................. 209
5.4 Feedback Systems: The Small-Gain Theorem .............. 217
5.5 Exercises .................................. 222
6 Passivity 227
6.1 Memoryless Functions ........................... 228
6.2 State Models ................................ 233
6.3 Positive Real Transfer Functions ..................... 237
6.4 L 2 and Lyapunov Stability ........................ 241
6.5 Feedback Systems: Passivity Theorems .................. 245
6.6 Exercises .................................. 259
7 Frequency Domain Analysis of Feedback Systems 263
7.1 Absolute Stability ............................. 264
7.1.1 Circle Criterion .......................... 265
7.1.2 Popov Criterion .......................... 275
7.2 The Describing Function Method ..................... 280
7.3 Exercises .................................. 296
8 Advanced Stability Analysis 303
8.1 The Center Manifold Theorem ...................... 303
8.2 Region of Attraction ............................ 312
8.3 Invariance-like Theorems ......................... 322
8.4 Stability of Periodic Solutions ....................... 329
8.5 Exercises .................................. 334
9 Stability of Perturbed Systems 339
9.1 Vanishing Perturbation .......................... 340
9.2 Nonvanishing Perturbation ........................ 346
9.3 Comparison Method ............................ 350
9.4 Continuity of Solutions on the Infinite Interval .............. 355
9.5 Interconnected Systems .......................... 358
9.6 Slowly Varying Systems .......................... 365
9.7 Exercises .................................. 372
10 Perturbation Theory and Averaging 381
10.1 The Perturbation Method ......................... 382
10.2 Perturbation on the Infinite Interval ................... 393
10.3 Periodic Perturbation of Autonomous Systems .............. 397
10.4 Averaging ................................. 402
10.5 Weakly Nonlinear Second-Order Oscillators ............... 411
10.6 General Averaging ............................. 413
10.7 Exercises .................................. 419
11 Singular Perturbations 423
11.1 The Standard Singular Perturbation Model ................ 424
11.2 Time-Scale Properties of the Standard Model .............. 430
11.3 Singular Perturbation on the Infinite Interval ............... 439
11.4 Slow and Fast Manifolds ......................... 443
11.5 Stability Analysis ............................. 449
11.6 Exercises .................................. 460
12 Feedback Control 469
12.1 Control Problems ............................. 469
12.2 Stabilization via Linearization ....................... 475
12.3 Integral Control .............................. 478
12.4 Integral Control via Linearization ..................... 481
12.5 Gain Scheduling .............................. 485
12.6 Exercises .................................. 499
13 Feedback Linearization 505
13.1 Motivation ................................. 505
13.2 Input–Output Linearization ........................ 509
13.3 Full-State Linearization .......................... 521
13.4 State Feedback Control .......................... 530
13.4.1 Stabilization ........................... 530
13.4.2 Tracking .............................. 540
13.5 Exercises .................................. 544
14 Nonlinear Design Tools 553
14.1 Sliding Mode Control ........................... 554
14.1.1 Motivating Example ....................... 554
14.1.2 Stabilization ........................... 565
14.1.3 Tracking .............................. 574
14.1.4 Regulation via Integral Control ................. 577
14.2 Lyapunov Redesign ............................ 581
14.2.1 Stabilization ............................ 581
14.2.2 Nonlinear Damping ....................... 590
14.3 Backstepping ............................... 591
14.4 Passivity-Based Control .......................... 606
14.5 High-Gain Observers ............................ 612
14.5.1 Motivating Example ....................... 614
14.5.2 Stabilization ........................... 621
14.5.3 Regulation via Integral Control ................. 625
14.6 Exercises .................................. 627
A Mathematical Review 649
B Contraction Mapping 655
C Proofs 659
C.1 Proof of Theorems 3.1 and 3.2 ...................... 659
C.2 Proof of Lemma 3.4 ............................ 661
C.3 Proof of Lemma 4.1 ............................ 663
C.4 Proof of Lemma 4.3 ............................ 664
C.5 Proof of Lemma 4.4 ............................ 664
C.6 Proof of Lemma 4.5 ............................ 665
C.7 Proof of Theorem 4.16 .......................... 667
C.8 Proof of Theorem 4.17 .......................... 671
C.9 Proof of Theorem 4.18 .......................... 677
C.10 Proof of Theorem 5.4 ........................... 678
C.11 Proof of Lemma 6.1 ............................ 679
C.12 Proof of Lemma 6.2 ............................ 682
C.13 Proof of Lemma 7.1 ............................ 686
C.14 Proof of Theorem 7.4 ........................... 690
C.15 Proof of Theorems 8.1 and 8.3 ...................... 692
C.16 Proof of Lemma 8.1 ............................ 701
C.17 Proof of Theorem 11.1 .......................... 702
C.18 Proof of Theorem 11.2 .......................... 708
C.19 Proof of Theorem 12.1 .......................... 710
C.20 Proof of Theorem 12.2 .......................... 711
C.21 Proof of Theorem 13.1 .......................... 712
C.22 Proof of Theorem 13.2 .......................... 714
C.23 Proof of Theorem 14.6 .......................... 715
Note and References 721
Bibliography 726
Symbols 742
Index 744
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menamine / 26.10.2009
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