Nonlinear Control Sy.. - Free

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LIST OF FIGURES 347 6.12 The nonlinearity 0(t*, x) in the sector [a,,3] .. . . . . . . . . . . . . . . . . . 178 7.1 Cascade connection of ISS systems...... ...... . . . .. . . . . . . . 195 7.2 Cascade connection of ISS systems with input u = 0 . . . . . . . . . . . . . . 197 8.1 Passive network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 ........... .. . 8.2 Passive network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 8.3 H=H1+H2+...+H.. . . . . . . . . . . . . . . 209 8.4 The Feedback System S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 8.5 The Feedback System S1 ............................. 211 8.6 The Feedback System S .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 9.1 A Passive system .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 9.2 Mass-spring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 9.3 Feedback interconnection . . . . .... ... . . . . . . . . .......... 240 9.4 Standard setup .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 9.5 Feedback Interconnection used in example 9.2 . . . . . . . . . . . . . . . . . 249 9.6 Standard setup .... . . . . . . . . . . . . . . . . . . . . A.1 Asymptotically stable equilibrium point.. . . . . ........... 250 ......... .. . . . . 308 A.2 Asymptotically stable equilibrium point . . . . . . . . . . . . . . . . . . . . . 309 A.3 Characteristics of H2 and H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 A.4 The feedback system Sf. . ... ......... . . . . . . . .. ... . . . . 327
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CONTROi I naiysis ana uesign (4)WIL
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Copyright © 2003 by John Wiley & S
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Contents 1 Introduction 1 1.1 Linea
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CONTENTS ix 3.8 The Invariance Prin
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CONTENTS xi 8.1 Power and Energy: P
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CONTENTS xiii A Proofs 307 A.1 Chap
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xvi 8, along with some of the most
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Chapter 1 Introduction This first c
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1.2. NONLINEAR SYSTEMS 3 with A=[-o
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1.3. EQUILIBRIUM POINTS 5 1.3 Equil
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1.4. FIRST-ORDER AUTONOMOUS NONLINE
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1.5. SECOND-ORDER SYSTEMS: PHASE-PL
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1.6. PHASE-PLANE ANALYSIS OF LINEAR
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1.7. PHASE-PLANE ANALYSIS OF NONLIN
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1.8. HIGHER-ORDER SYSTEMS 1.8.1 Cha
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1.9. EXAMPLES OF NONLINEAR SYSTEMS
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1.9. EXAMPLES OF NONLINEAR SYSTEMS
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1.10. EXERCISES 27 Figure 1.18: Bal
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1.10. EXERCISES 29 m2 Figure 1.19:
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Chapter 2 Mathematical Preliminarie
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2.3. VECTOR SPACES 33 (3) 3 0 E X :
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2.3. VECTOR SPACES 35 where the 1 e
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2.3. VECTOR SPACES 37 Proof: First
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2.4. MATRICES 39 2.4 Matrices We as
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2.4. MATRICES 41 Proof: By definiti
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2.4. MATRICES 43 (i) A is positive
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2.6. SEQUENCES 45 Compact set: A se
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2.7. FUNCTIONS 47 If f is a functio
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2.8. DIFFERENTIABILITY 2.8 Differen
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2.8. DIFFERENTIABILITY 51 Theorem 2
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2.9. LIPSCHITZ CONTINUITY 53 Notice
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2.10. CONTRACTION MAPPING 55 and th
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2.11. SOLUTION OF DIFFERENTIAL EQUA
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2.12. EXERCISES 59 Denoting t1 = to
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2.12. EXERCISES 61 (2.10) Show that
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2.12. EXERCISES 63 Notes and Refere
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66 CHAPTER 3. LYAPUNOV STABILITY I.
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72 CHAPTER 3. LYAPUNOV STABILITY I:
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100 CHAPTER 3. LYAPUNOV STABILITY I
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108 CHAPTER 4. LYAPUNOV STABILITY H
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126 CHAPTER 4. LYAPUNOV STABILITY H
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Chapter 5 Feedback Systems So far,
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5.1. BASIC FEEDBACK STABILIZATION 1
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5.2. INTEGRATOR BACKSTEPPING 141 5.
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5.2. INTEGRATOR BACKSTEPPING 143 De
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5.3. BACKSTEPPING: MORE GENERAL CAS
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5.4. EXAMPLE 151 5.4 Example 8 Figu
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5.5. EXERCISES 153 [S - 0(x)] = x1
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Chapter 6 Input-Output Stability So
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6.1. FUNCTION SPACES 157 Both L2 an
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6.2. INPUT-OUTPUT STABILITY 159 Thu
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6.2. INPUT-OUTPUT STABILITY 161 (a)
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6.2. INPUT-OUTPUT STABILITY 163 1.2
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6.3. LINEAR TIME-INVARIANT SYSTEMS
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6.4. L GAINS FOR LTI SYSTEMS where
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6.5. CLOSED-LOOP INPUT-OUTPUT STABI
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6.6. THE SMALL GAIN THEOREM 171 In
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6.6. THE SMALL GAIN THEOREM 173 N(x
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6.7. LOOP TRANSFORMATIONS 175 Figur
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6.7. LOOP TRANSFORMATIONS 177 U l M
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6.8. THE CIRCLE CRITERION 179 (i) g
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6.9. EXERCISES 181 (6.3) Prove the
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Chapter 7 Input-to-State Stability
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7.2. DEFINITIONS 185 Setting u = 0,
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7.3. INPUT-TO-STATE STABILITY (ISS)
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7.3. INPUT-TO-STATE STABILITY (ISS)
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7.4. INPUT-TO-STATE STABILITY REVIS
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7.4. INPUT-TO-STATE STABILITY REVIS
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7.5. CASCADE-CONNECTED SYSTEMS U E2
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7.5. CASCADE-CONNECTED SYSTEMS 197
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7.6. EXERCISES 199 (i) Is it locall
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202 CHAPTER 8. PASSIVITY v i Figure
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204 CHAPTER 8. PASSIVITY Moreover,
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206 CHAPTER 8. PASSIVITY Definition
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208 CHAPTER 8. PASSIVITY Thus (UT,
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210 CHAPTER 8. PASSIVITY Thus, H f
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212 CHAPTER 8. PASSIVITY Under thes
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214 CHAPTER 8. PASSIVITY Under thes
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216 CHAPTER 8. PASSIVITY (i) H is p
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218 CHAPTER 8. PASSIVITY Definition
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220 CHAPTER 8. PASSIVITY Example 8.
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Chapter 9 Dissipativity In Chapter
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9.2. DIFFERENTIABLE STORAGE FUNCTIO
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9.3. QSR DISSIPATIVITY 227 Definiti
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9.4. EXAMPLES 229 5- Very strictly-
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9.5. AVAILABLE STORAGE 9.4.2 Mass-S
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9.6. ALGEBRAIC CONDITION FOR DISSIP
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9.6. ALGEBRAIC CONDITION FOR DISSIP
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9.7. STABILITY OF DISSIPATIVE SYSTE
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9.8. FEEDBACK INTERCONNECTIONS 239
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9.8. FEEDBACK INTERCONNECTIONS 241
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9.9. NONLINEAR G2 GAIN 9.9 Nonlinea
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9.9. NONLINEAR L2 GAIN 245 (iii) IH
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9.10. SOME REMARKS ABOUT CONTROL DE
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9.10. SOME REMARKS ABOUT CONTROL DE
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9.11. NONLINEAR L2-GAIN CONTROL 251
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9.12. EXERCISES 253 9.12 Exercises
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Chapter 10 Feedback Linearization I
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10.1. MATHEMATICAL TOOLS 257 Lfh(x)
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10.1. MATHEMATICAL TOOLS 259 10.1.3
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10.1. MATHEMATICAL TOOLS 261 and su
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10.1. MATHEMATICAL TOOLS 263 Defini
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10.2. INPUT-STATE LINEARIZATION 265
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10.2. INPUT-STATE LINEARIZATION 267
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10.2. INPUT-STATE LINEARIZATION and
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10.3. EXAMPLES 271 provided that wh
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10.4. CONDITIONS FOR INPUT-STATE LI
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10.5. INPUT-OUTPUT LINEARIZATION 27
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10.6. THE ZERO DYNAMICS 281 i=Ax+Bu
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10.6. THE ZERO DYNAMICS 283 that th
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10.6. THE ZERO DYNAMICS 285 Definit
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10.7. CONDITIONS FOR INPUT-OUTPUT L
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10.8. EXERCISES 289 (10.8) Consider
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292 CHAPTER 11. NONLINEAR OBSERVERS
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294 CHAPTER 11. NONLINEAR OBSERVERS
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Page 325 and 326: 308 APPENDIX A. PROOFS (ii) It is c
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Page 339 and 340: 322 APPENDIX A. PROOFS To this end
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Page 349 and 350: 332 APPENDIX A. PROOFS Assume now t
Page 351 and 352: 334 APPENDIX A. PROOFS Multiplying
Page 354 and 355: Bibliography [1] B. D. O. Anderson
Page 356 and 357: BIBLIOGRAPHY 339 [27] W. Hahn, Stab
Page 358 and 359: BIBLIOGRAPHY 341 [58] E. Ott, Chaos
Page 360: BIBLIOGRAPHY 343 [87] A. van der Sc
Page 363: 346 LIST OF FIGURES 3.1 Stable equi
Page 367 and 368: 350 globally uniformly asymptotical
Page 369: 352 Subspaces, 36 Supply rate, 224
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