Nonlinear systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Prentice Hall
1996
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 734 S. graph. Darst. |
| ISBN: | 0132280248 |
Internformat
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| 245 | 1 | 0 | |a Nonlinear systems |c Hassan K. Khalil |
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| 264 | 1 | |a Upper Saddle River, NJ |b Prentice Hall |c 1996 | |
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Datensatz im Suchindex
| _version_ | 1804125649406787584 |
|---|---|
| adam_text | Titel: Nonlinear systems
Autor: Khalil, Hassan K
Jahr: 1996
Contents 1 Introduction 1 1.1 Examples............................. 5 1.1.1 Pendulum Equation................... 5 1.1.2 Tunnel Diode Circuit.................. 7 1.1.3 Mass-Spring System . . ................ 8 1.1.4 Negative-Resistance Oscillator............. 11 1.1.5 Artificial Neural Network................ 14 1.1.6 Adaptive Control .................... 16 1.2 Second-Order Systems...................... 19 1.2.1 Qualitative Behavior of Linear Systems......... 23 1.2.2 Multiple Equilibria.................... 33 1.2.3 Qualitative Behavior Near Equilibrium Points..... 36 1.2.4 Limit Cycles....................... 41 1.2.5 Numerical Construction of Phase Portraits....... 46 1.3 Exercises............................. 47 2 Fundamental Properties 57 2.1 Mathematical Preliminaries................... 58 2.1.1 Euclidean Space..................... 58 2.1.2 Mean Value and Implicit Function Theorems...... 62 2.1.3 Gronwall-Bellman Inequality .............. 63 2.1.4 Contraction Mapping.................. 64 2.2 Existence and Uniqueness.................... 67 2.3 Continuous Dependence on Initial Conditions and Parameters......................... 78 2.4 Differentiability of Solutions and Sensitivity Equations ............................ 81 2.5 Comparison Principle...................... 84 2.6 Exercises............................. 88 IX
X 3 Lyapunov Stability 97 3.1 Autonomous Systems...................... 98 3.2 The Invariance Principle..................... 113 3.3 Linear Systems and Linearization................ 120 3.4 Nonautonomous Systems.................... 132 3.5 Linear Time-Varying Systems and Linearization........ 143 3.6 Converse Theorems....................... 148 3.7 Exercises............................. 154 4 Advanced Stability Analysis 167 4.1 The Center Manifold Theorem................. 167 4.2 Region of Attraction....................... 177 4.3 Invariance Theorems....................... 191 4.4 Exercises............................. 196 5 Stability of Perturbed Systems 203 5.1 Vanishing Perturbation ..................... 204 5.2 Nonvanishing Perturbation ................... 211 5.3 Input-to-State Stability..................... 217 5.4 Comparison Method.......... 222 5.5 Continuity of Solutions on the Infinite Interval......... 228 5.6 Interconnected Systems..................... 230 5.7 Slowly Varying Systems..................... 239 5.8 Exercises............................. 250 6 Input-Output Stability 261 6.1 C Stability............................ 262 6.2 C Stability of State Models................... 269 6.3 Input-to-Output Stability.................... 275 6.4 £2 Gain............................. 276 6.5 Exercises............................. 284 7 Periodic Orbits 289 7.1 Second-Order Systems...................... 289 7.2 Stability of Periodic Solutions.................. 299 7.3 Exercises............................. 309 8 Perturbation Theory and Averaging 313 8.1 The Perturbation Method.............. 314 8.2 Perturbation on the Infinite Interval .............. 326 8.3 Averaging............................ 330 8.4 Weakly Nonlinear Second-Order Oscillators ........339
xi 8.5 General Averaging ........................ 342 8.6 Exercises ............................. 347 9 Singular Perturbations 351 9.1 The Standard Singular Perturbation Model........... 352 9.2 Time-Scale Properties of the Standard Model......... 358 9.3 Slow and Fast Manifolds .................... 365 9.4 Stability Analysis ........................ 372 9.5 Singular Perturbation on the Infinite Interval.......... 384 9.6 Exercises............................. 388 10 Analysis of Feedback Systems 399 10.1 Absolute Stability........................ 400 10.1.1 Circle Criterion ..................... 407 10.1.2 Popov Criterion..................... 419 10.1.3 Simultaneous Lyapunov Functions........... 423 10.2 Small-Gain Theorem.......................430 10.3 Passivity Approach ....................... 436 10.4 The Describing Function Method................ 450 10.5 Exercises............................. 468 11 Feedback Control 479 11.1 Control Problems........................ 479 11.2 Design via Linearization..................... 485 11.2.1 Stabilization ...................... 485 11.2.2 Regulation via Integral Control............ 488 11.3 Gain Scheduling......................... 493 11.4 Exercises............................. 509 12 Exact Feedback Linearization 519 12.1 Input-State Linearization .................... 519 12.2 Input-Output Linearization ................... 531 12.3 State Feedback Control..................... 545 12.3.1 Stabilization ...................... 545 12.3.2 Tracking......................... 552 12.3.3 Regulation via Integral Control ............ 554 12.4 Differential Geometric Approach ................ 558 12.4.1 Differential Geometric Tools .............. 558 12.4.2 Input-Output Linearization.............. 564 12.4.3 Input-State Linearization ............... 567 12.5 Exercises............................. 570
xii 13 Lyapunov-Based Design 577 13.1 Lyapunov Redesign ....................... 578 13.1.1 Robust Stabilization................... 578 13.1.2 Nonlinear Damping .................. 586 13.2 Backstepping .......................... 588 13.3 Sliding Mode Control...................... 601 13.4 Adaptive Control ........................ 617 13.4.1 Model Reference Controller.............. 618 13.4.2 Model Reference Adaptive Control.......... 622 13.5 Exercises............................. 640 Appendix A 651 A.l Proof of Lemma 2.5....................... 651 A.2 Proof of Lemma 3.1....................... 652 A.3 Proof of Lemma 3.3....................... 653 A.4 Proof of Lemma 3.4....................... 656 A.5 Proof of Lemma 3.5....................... 657 A.6 Proof of Theorem 3.14..................... 657 A.7 Proof of Theorems 4.1 and 4.3................. 661 A.8 Proof of Lemma 4.1....................... 668 A.9 Proof of Theorem 6.4...................... 669 A.10 Proof of Theorem 7.1...................... 671 A.11 Proof of Theorem 8.2...................... 674 A.12 Proof of Theorem 8.3...................... 676 A.13 Proof of Theorem 8.4...................... 680 A.14 Proof of Theorem 9.1...................... 681 A.15 Proof of Theorem 9.4...................... 686 A.16 Proof of Lemma 10.1...................... 688 A.17 Proof of Lemma 10.2...................... 691 A.18 Proof of Lemma 10.7...................... 694 A. 19 Proof of Theorem 10.9..................... 698 A.20 Proof of Lemma 13.4...................... 701 A.21 Proof of Lemma 13.5...................... 704 Notes and References 705 Bibliography 711 Symbols 725 Index 727
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| discipline | Informatik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed. |
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| spelling | Khalil, Hassan K. Verfasser aut Nonlinear systems Hassan K. Khalil 2. ed. Upper Saddle River, NJ Prentice Hall 1996 XII, 734 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Nichtlineares System (DE-588)4042110-7 s DE-604 Regelungstheorie (DE-588)4122327-5 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007478148&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khalil, Hassan K. Nonlinear systems Regelungstheorie (DE-588)4122327-5 gnd Nichtlineares System (DE-588)4042110-7 gnd |
| subject_GND | (DE-588)4122327-5 (DE-588)4042110-7 (DE-588)4123623-3 |
| title | Nonlinear systems |
| title_auth | Nonlinear systems |
| title_exact_search | Nonlinear systems |
| title_full | Nonlinear systems Hassan K. Khalil |
| title_fullStr | Nonlinear systems Hassan K. Khalil |
| title_full_unstemmed | Nonlinear systems Hassan K. Khalil |
| title_short | Nonlinear systems |
| title_sort | nonlinear systems |
| topic | Regelungstheorie (DE-588)4122327-5 gnd Nichtlineares System (DE-588)4042110-7 gnd |
| topic_facet | Regelungstheorie Nichtlineares System Lehrbuch |
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