Nonlinear systems: analysis, stability, and control
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
1999
|
| Series: | Interdisciplinary applied mathematics
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 667 S. graph. Darst. |
| ISBN: | 0387985131 |
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MARC
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| 100 | 1 | |a Sastry, Shankar |d 1956- |e Verfasser |0 (DE-588)121291057 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear systems |b analysis, stability, and control |c Shankar Sastry |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1999 | |
| 300 | |a XXV, 667 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Interdisciplinary applied mathematics |v 10 | |
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Record in the Search Index
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| adam_text |
Contents
Preface
vii
Acknowledgments
xi
Standard
Notation
xxiii
1
Linear
vs. Nonlinear
1
1.1
Nonlinear Models
. 1
1.2
Complexity in Nonlinear Dynamics
. 4
1.2.1
Subtleties of Nonlinear Systems Analysis
. 10
1.2.2
Autonomous Systems and Equilibrium Points
. 12
1.3
Some Classical Examples
. 14
1.3.1
The Tunnel Diode Circuit
. 14
1.3.2
An Oscillating Circuit Due to van
der
Pol
. 16
1.3.3
ThePendulum: DuetoNewton
. 17
1.3.4
The Buckling Beam: Due to
Euler
. 19
1.3.5
The Volterra-Lotka Predator-Prey Equations
. 22
1.4
Other Classics: Musical Instruments
. 23
1.4.1
Blowing of a Clarinet Reed: Due to Rayleigh
. 23
1.4.2
Bowing of
a'Wolin
String: Due to Rayleigh
. 23
1.5
Summary
. 25
1.6
Exercises
. 26
2
Planar Dynamical Systems
31
2.1
Introduction
. 31
2.2
Linearization About Equilibria of Second-Order
Nonlinear Systems
. 31
xvi Contents
2.2.1 Linear Systems in
the Plane
. 32
2.2.2 Phase
Portraits near Hyperbolic Equilibria
. 36
2.3
Closed Orbits of Planar Dynamical Systems
. 41
2.4
Counting Equilibria: Index Theory
. 49
2.5
Bifurcations
. 51
2.6
Bifurcation Study of
Josephson
Junction Equations
. 55
2.7
The Degenerate van
der Pol
Equation
. 60
2.8
Planar Discrete-Time Systems
. 63
2.8.1
Fixed Points and the Hartman-Grobman Theorem
. 63
2.8.2
Period
N
Points of Maps
. 65
2.8.3
Bifurcations of Maps
. 66
2.9
Summary
. 69
2.10
Exercises
. 69
3
Mathematical Background
76
3.1
Groups and Fields
. 76
3.2
Vector Spaces, Algebras, Norms, and Induced Norms
. 77
3.3
Contraction Mapping Theorems
. 82
3.3.1
Incremental Small Gain Theorem
. 84
3.4
Existence and Uniqueness Theorems for
Ordinary Differential Equations
. 86
3.4.1
Dependence on Initial Conditions on
Infinite Time Intervals
. 90
3.4.2
Circuit Simulation by Waveform Relaxation
. 90
3.5
Differential Equations with Discontinuities
. 93
3.6
Carleman
Linearization
. 99
3.7
Degree Theory
. 101
3.8
Degree Theory and Solutions of Resistive Networks
. 105
3.9
Basics of Differential Topology
. 107
3.9.1
Smooth Manifolds and Smooth Maps
. 107
3.9.2
Tangent Spaces and Derivatives
. 110
3.9.3
Regular Values
. 113
3.9.4
Manifolds with Boundary
. 115
3.10
Summary
. 118
3.11
Exercises
. 119
4
Input-Output Analysis
127
4.1
Optimal Linear Approximants to Nonlinear Systems
. 128
4.1.1
Optimal Linear Approximations for Memoryless,
Time-Invariant Nonlinearities
. 132
4.1.2
Optimal Linear Approximations for Dynamic
Nonlinearities: Oscillations in Feedback Loops
. 135
4.1.3
Justification of the Describing Function
. 138
4.2
Input-Output Stability
. 143
4.3
Applications of the Small Gain Theorems
. 150
Contents xvii
4.3.1
Robustness of
Feedback
Stability
. 150
4.3.2
Loop Transformation Theorem
. 152
4.4
Passive Nonlinear Systems
.
]53
4.5
Input-Output Stability of Linear Systems
. 156
4.6
Input-Output Stability Analysis of Feedback Systems
. 160
4.6.1
The Lur'e Problem
. 162
4.7
Volterra Input-Output Representations
. 167
4.7.1
Homogeneous, Polynomial and Volterra Systems in
the Time Domain
. 168
4.7.2
Volterra Representations from Differential Equations
. 170
4.7.3
Frequency Domain Representation of Volterra Input
Output Expansions
. 173
4.8
Summary
. 174
4.9
Exercises
. 175
5
Lyapunov Stability Theory
182
5.1
Introduction
. 182
5.2
Definitions
. 183
5.2.1
The Lipschitz Condition and Consequences
. 183
5.3
Basic Stability Theorems of Lyapunov
. 188
5.3.1
Energy-Like Functions
. 188
5.3.2
Basic Theorems
. 189
5.3.3
Examples of the Application of Lyapunov's Theorem
. 192
5.3.4
Exponential Stability Theorems
. 195
5.4
LaSalle's
Invariance
Principle
. 198
5.5
Generalizations of LaSalle's Principle
. 204
5.6
Instability Theorems
. 206
5.7
Stability of Linear Time-Varying Systems
. 207
5.7.1
Autonomous Linear Systems
. 209
5.7.2
Quadratic Lyapunov Functions for Linear Time
Varying Systems
. 212
5.8
The Indirect Method of Lyapunov
. 214
5.9
Domains of Attraction
. 217
5.10
Summary
. 223
5.11
Exercises
. 223
6
Applications of Lyapunov Theory
235
6.1
Feedback Stabilization
. 235
6.2
The Lur'e Problem, Circle and Popov Criteria
. 237
6.2.1
The Circle Criterion
. 240
6.2.2
The Popov Criterion
. 245
6.3
Singular Perturbation
. 247
6.3.1
Nonsingular Points, Solution Concepts, and
Jump Behavior
. 250
6.4
Dynamics of Nonlinear Systems and Parasitics
. 252
xviii Contents
6.4.1 Dynamics
of Nonlinear
Circuits
. 252
6.4.2
Dynamics
of
Power Systems
. 255
6.5
Adaptive
Identification
of Single-Input Single-Output Linear
Time-Invariant Systems
. 256
6.5.1
Linear Identifier Stability
. 262
6.5.2
Parameter Error Convergence
. 265
6.6
Averaging
. 266
6.7
Adaptive Control
. 273
6.8
Back-stepping Approach to Stabilization
. 275
6.9
Summary
. 277
6.10
Exercises
. 278
7
Dynamical Systems and Bifurcations
287
7.1
Qualitative Theory
. 287
7.2
Nonlinear Maps
. 291
7.3
Closed Orbits,
Poincaré
Maps, and Forced Oscillations
. 294
7.3.1
The
Poincaré Map
and Closed Orbits
. 294
7.3.2
The
Poincaré Map
and Forced Oscillations
. 297
7.4
Structural Stability
. 302
7.5
Structurally Stable Two Dimensional Flows
. 305
7.6
Center Manifold Theorems
. 309
7.6.1
Center Manifolds for Flows
. 309
7.6.2
Center Manifolds for Flows Depending on Parameters
. 313
7.6.3
Center Manifolds for Maps
. 314
7.7
Bifurcation of Vector Fields: An Introduction
. 315
7.8
Bifurcations of Equilibria of Vector Fields
. 317
7.8.1
Single, Simple Zero Eigenvalue
. 317
7.8.2
Pure Imaginary Pair of Eigenvalues:
Poincaré-Andronov-Hopf
Bifurcation
. 322
7.9
Bifurcations of Maps
. 324
7.9.1
Single Eigenvalue
1:
Saddle Node,
Transcriticai
and Pitchfork
. 325
7.9.2
Single Eigenvalue
-1:
Period Doubling
. 327
7.9.3
Pair of Complex Eigenvalues of Modulus
1:
Naimark-Sacker Bifurcation
. 328
7.10
More Complex Bifurcations of Vector Fields and Maps
. 329
7.10.1
Bifurcations of Equilibria and Fixed Points:
Catastrophe Theory
. 329
7.10.2
Singular Perturbations and Jump Behavior of Systems
. 335
7.10.3
Dynamic Bifurcations: A Zoo
. 337
7.11
Routes to Chaos and Complex Dynamics
. 340
7.12
Exercises
. 341
8
Basics of Differential Geometry
349
8.1
TangentSpaces
. 349
Contents xix
8.1.1
Vector
Fields, Lie Brackets, and Lie Algebras
. 352
8.2
Distributions and Codistributions
. 356
8.3
Frobenius Theorem
. 359
8.4
Matrix Groups
. 362
8.4.1
Matrix Lie Groups and Their Lie Algebras
. 367
8.4.2
The Exponential Map
. 369
8.4.3
Canonical Coordinates on Matrix Lie Groups
. 370
8.4.4
The Campbell-Baker-Hausdorff Formula
. 371
8.5
Left-Invariant Control Systems on Matrix Lie Groups
. 375
8.5.1
Frenet-Serret Equations: A Control System on
SE
(3) . 375
8.5.2
The Wei-Norman Formula
. 378
8.6
Summary
. 379
8.7
Exercises
. 379
9
Linearization by State Feedback
384
9.1
Introduction
. 384
9.2
SISO
Systems
. 385
9.2.1
Input-Output Linearization
. 385
9.2.2
Zero Dynamics for
SISO
Systems
. 398
9.2.3
Inversion and Exact Tracking
. 402
9.2.4
Asymptotic Stabilization and Tracking for
SISO
Systems
. 404
9.3
MIMO
Systems
. 407
9.3.1
MIMO
Systems Linearizable by Static State Feedback
. 407
9.3.2
Full State Linearization of
MIMO
Systems
. 411
9.3.3
Dynamic Extension for
MIMO
Systems
. 414
9.4
Robust Linearization
.
4J7
9.5
Sliding Mode Control
. 423
9.5.1
SISO
Sliding Mode Control
. 423
9.5.2
MIMO
Sliding Mode Control
. 425
9.6
Tracking for
Nonminimum
Phase Systems
. 425
9.6.1
The Method of Devasia, Chen, and
Paden
. 426
9.6.2
The Byrnes-Isidori Regulator
. 429
9.7
Observers with Linear Error Dynamics
. 433
9.8
Summary
. 439
9.9
Exercises
. 440
10
Design Examples Using Linearization
449
10.1
Introduction
. 449
10.2
The Ball and Beam Example
. 450
10.2.1
Dynamics
. 451
10.2.2
Exact Input-Output Linearization
. 451
10.2.3
Full State Linearization
. 453
10.2.4
Approximate Input-Output Linearization
. 454
10.2.5
Switching Control of the Ball and Beam System
. 458
xx
Contents
10.3
Approximate Linearization for Nonregular
SISO
Systems
. . . 460
10.3.1
Tracking for Nonregular Systems
. 468
10.4
Nonlinear Right Control
. 468
10.4.1
Force and Moment Generation
. 469
10.4.2
Simplification to a Planar Aircraft
. 472
10.4.3
Exact Input-Output Linearization of the PVTOL
Aircraft System
. 473
10.4.4
Approximate Linearization of the PVTOL Aircraft
. . 476
10.5
Control of Slightly Nonminimum Phase Systems
. 481
10.5.1
Single Input Single Output
(SISO)
Case
. 481
10.5.2
Generalization to
MIMO
Systems
. 484
10.6
Singularly Perturbed Zero Dynamics for Regularly Perturbed
Nonlinear Systems
. 490
10.6.1
SISO
Singularly Perturbed Zero and Driven Dynamics
. 490
10.6.2
MIMO
Singularly Perturbed Zero and
Driven Dynamics
. 493
10.7
Summary
. 498
10.8
Exercises
. 499
11
Geometric Nonlinear Control
510
11.1
Controllability Concepts
. 510
11.2
Drift-Free Control Systems
. 513
11.3
Steering of Drift-Free Nonholonomic Systems
. 518
11.4
Steering Model Control Systems Using Sinusoids
. 520
11.5
General Methods for Steering
. 529
11.5.1
Fourier Techniques
. 529
11.5.2
Optimal Steering of Nonholonomic Systems
. 535
11.5.3
Steering with Piecewise Constant Inputs
. 539
11.5.4
Control Systems with Drift
. 545
11.6
Observability Concepts
. 549
11.7
Zero Dynamics Algorithm and Generalized Normal Forms
. 551
11.8
Input-Output Expansions for Nonlinear Systems
. 560
11.9
Controlled Invariant Distributions and Disturbance Decoupling
. 564
11.10
Summary
. 566
11.11
Exercises
. 567
12
Exterior Differential Systems in Control
574
12.1
Introduction
. 574
12.2
Introduction to Exterior Differential Systems
. 575
12.2.1
Multilinear Algebra
. 576
12.2.2
Forms
. 592
12.2.3
Exterior Differential Systems
. 600
12.3
Normal Forms
. 606
12.3.1
The Goursat Normal Form
. 606
12.3.2
The
л
-trailer
Pfaffian System
.,. 614
Contents xxi
12.3.3
The Extended Goursat Normal Form
. 623
12.4
Control Systems
. 629
12.5
Summary
. 635
12.6
Exercises
. 636
13
New Vistas: Multi-Agent Hybrid Systems
641
13.1
Embedded Control and Hybrid Systems
. 641
13.2
Multi-
Agent Systems and Hybrid Systems
. 642
References
645
Index
661 |
| any_adam_object | 1 |
| author | Sastry, Shankar 1956- |
| author_GND | (DE-588)121291057 |
| author_facet | Sastry, Shankar 1956- |
| author_role | aut |
| author_sort | Sastry, Shankar 1956- |
| author_variant | s s ss |
| building | Verbundindex |
| bvnumber | BV012712962 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.S35157 1999 |
| callnumber-search | QA402.S35157 1999 |
| callnumber-sort | QA 3402 S35157 41999 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 810 SK 880 SK 960 |
| classification_tum | MAT 344f MAT 345f MAT 587f |
| ctrlnum | (OCoLC)246032907 (DE-599)BVBBV012712962 |
| dewey-full | 003.75 003/.7521 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.75 003/.75 21 |
| dewey-search | 003.75 003/.75 21 |
| dewey-sort | 13.75 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV012712962 |
| illustrated | Illustrated |
| indexdate | 2024-08-27T00:21:13Z |
| institution | BVB |
| isbn | 0387985131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008641957 |
| oclc_num | 246032907 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-29T DE-473 DE-BY-UBG DE-521 DE-20 DE-634 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-384 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-29T DE-473 DE-BY-UBG DE-521 DE-20 DE-634 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XXV, 667 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | Sastry, Shankar 1956- Verfasser (DE-588)121291057 aut Nonlinear systems analysis, stability, and control Shankar Sastry New York, NY [u.a.] Springer 1999 XXV, 667 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 10 Nichtlineares System Nonlinear systems System analysis Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Dynamisches Verhalten (DE-588)4140475-0 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Rückkopplung (DE-588)4050851-1 gnd rswk-swf Systemanalyse (DE-588)4116673-5 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Linearisierung (DE-588)4199872-8 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s Dynamisches Verhalten (DE-588)4140475-0 s Systemanalyse (DE-588)4116673-5 s DE-604 Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Verzweigung Mathematik (DE-588)4078889-1 s Rückkopplung (DE-588)4050851-1 s Kontrolltheorie (DE-588)4032317-1 s Linearisierung (DE-588)4199872-8 s Interdisciplinary applied mathematics 10 (DE-604)BV004216726 10 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008641957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sastry, Shankar 1956- Nonlinear systems analysis, stability, and control Interdisciplinary applied mathematics Nichtlineares System Nonlinear systems System analysis Kontrolltheorie (DE-588)4032317-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Dynamisches Verhalten (DE-588)4140475-0 gnd Nichtlineares System (DE-588)4042110-7 gnd Rückkopplung (DE-588)4050851-1 gnd Systemanalyse (DE-588)4116673-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Linearisierung (DE-588)4199872-8 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4078889-1 (DE-588)4140475-0 (DE-588)4042110-7 (DE-588)4050851-1 (DE-588)4116673-5 (DE-588)4167992-1 (DE-588)4199872-8 |
| title | Nonlinear systems analysis, stability, and control |
| title_auth | Nonlinear systems analysis, stability, and control |
| title_exact_search | Nonlinear systems analysis, stability, and control |
| title_full | Nonlinear systems analysis, stability, and control Shankar Sastry |
| title_fullStr | Nonlinear systems analysis, stability, and control Shankar Sastry |
| title_full_unstemmed | Nonlinear systems analysis, stability, and control Shankar Sastry |
| title_short | Nonlinear systems |
| title_sort | nonlinear systems analysis stability and control |
| title_sub | analysis, stability, and control |
| topic | Nichtlineares System Nonlinear systems System analysis Kontrolltheorie (DE-588)4032317-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Dynamisches Verhalten (DE-588)4140475-0 gnd Nichtlineares System (DE-588)4042110-7 gnd Rückkopplung (DE-588)4050851-1 gnd Systemanalyse (DE-588)4116673-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Linearisierung (DE-588)4199872-8 gnd |
| topic_facet | Nichtlineares System Nonlinear systems System analysis Kontrolltheorie Verzweigung Mathematik Dynamisches Verhalten Rückkopplung Systemanalyse Ljapunov-Stabilitätstheorie Linearisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008641957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
| work_keys_str_mv | AT sastryshankar nonlinearsystemsanalysisstabilityandcontrol |