Nonlinear Control Sy.. - Free

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author who may feel that his or her work has not been properly acknowledged here and encourage them to write to me. I am deeply grateful to the University of Alberta for providing me with an excellent working environment and to the Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting my research. I am also thankful to John Wiley and Son's representatives: John Telecki, Kristin Cooke Fasano, Kirsten Rohstedt and Brendan Cody, for their professionalism and assistance. I would like to thank my wife Goody for her encouragement during the writing of this book, as well as my son Francisco and my daughter Madison. To all three of them I owe many hours of quality time. Guess what guys? It's over (until the next project). Tonight I'll be home early. Edmonton, Alberta xvii Horacio J. Marquez
Page 1 and 2: CONTROi I naiysis ana uesign (4)WIL
Page 3 and 4: Copyright © 2003 by John Wiley & S
Page 6 and 7: Contents 1 Introduction 1 1.1 Linea
Page 8 and 9: CONTENTS ix 3.8 The Invariance Prin
Page 10 and 11: CONTENTS xi 8.1 Power and Energy: P
Page 12: CONTENTS xiii A Proofs 307 A.1 Chap
Page 15: xvi 8, along with some of the most
Page 19 and 20: 2 CHAPTER 1. INTRODUCTION Figure 1.
Page 21 and 22: 4 CHAPTER 1. INTRODUCTION This equa
Page 23 and 24: 6 CHAPTER 1. INTRODUCTION case, whi
Page 25 and 26: 8 Figure 1.3: The system ± = r + x
Page 27 and 28: 10 CHAPTER 1. INTRODUCTION l' `.\ \
Page 29 and 30: 12 CHAPTER 1. INTRODUCTION Figure 1
Page 33 and 34: 16 CHAPTER 1. INTRODUCTION From her
Page 35 and 36: 18 CHAPTER 1. INTRODUCTION 1.7 Phas
Page 37 and 38: 20 C T Figure 1.12: Nonlinear RLC-c
Page 41 and 42: 24 CHAPTER 1. INTRODUCTION This mod
Page 45 and 46: 28 (a) (b) (c) (d) (e) (f) (g) [i2J
Page 47 and 48: 30 CHAPTER 1. INTRODUCTION Notes an
Page 49 and 50: 32 CHAPTER 2. MATHEMATICAL PRELIMIN
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50 CHAPTER 2. MATHEMATICAL PRELIMIN
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58 It follows that CHAPTER 2. MATHE
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60 CHAPTER 2. N ATHEMATICAL PRELIMI
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Chapter 3 Lyapunov Stability I: Aut
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3.1. DEFINITIONS 67 Figure 3.2: Asy
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3.2. POSITIVE DEFINITE FUNCTIONS 69
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3.3. STABILITY THEOREMS 71 system o
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3.3. STABILITY THEOREMS 73 In other
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3.4. EXAMPLES where l is the length
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3.5. ASYMPTOTIC STABILITY IN THE LA
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3.5. ASYMPTOTIC STABILITY IN THE LA
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3.6. POSITIVE DEFINITE FUNCTIONS RE
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3.7. CONSTRUCTION OF LYAPUNOV FUNCT
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3.8. THE INVARIANCE PRINCIPLE Step
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3.8. THE INVARIANCE PRINCIPLE 87 De
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3.8. THE INVARIANCE PRINCIPLE 89 an
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3.8. THE INVARIANCE PRINCIPLE 91 bo
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3.9. REGION OF ATTRACTION 93 We can
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3.9. REGION OF ATTRACTION 95 Figure
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3.10. ANALYSIS OF LINEAR TIME-INVAR
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3.10. ANALYSIS OF LINEAR TIME-INVAR
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3.11. INSTABILITY 101 (i) V(0) = 0
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3.12. EXERCISES 103 (a) Find all of
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3.12. EXERCISES (3.8) Prove the fol
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Chapter 4 Lyapunov Stability II: No
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4.1. DEFINITIONS 109 All of these d
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4.2. POSITIVE DEFINITE FUNCTIONS 11
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4.3. STABILITY THEOREMS 113 Thus, W
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4.4. PROOF OF THE STABILITY THEOREM
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4.4. PROOF OF THE STABILITY THEOREM
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4.5. ANALYSIS OF LINEAR TIME-VARYIN
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4.5. ANALYSIS OF LINEAR TIME-VARYIN
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4.6. PERTURBATION ANALYSIS 123 and
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4.7. CONVERSE THEOREMS that is Amin
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4.9. DISCRETIZATION 127 4.9 Discret
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4.9. DISCRETIZATION 129 differentia
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4.10. STABILITY OF DISCRETE-TIME SY
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4.11. EXERCISES 133 To study the st
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4.11. EXERCISES 135 xl ±2 = x2 + x
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138 CHAPTER 5. FEEDBACK SYSTEMS 5.1
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140 CHAPTER 5. FEEDBACK SYSTEMS (i)
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142 a) b) c) d) U U U -O(x) z CHAPT
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144 CHAPTER 5. FEEDBACK SYSTEMS Thu
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146 CHAPTER 5. FEEDBACK SYSTEMS G-1
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148 CHAPTER 5. FEEDBACK SYSTEMS In
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150 CHAPTER 5. FEEDBACK SYSTEMS Wit
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152 CHAPTER 5. FEEDBACK SYSTEMS alo
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154 CHAPTER 5. FEEDBACK SYSTEMS (5.
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156 CHAPTER 6. INPUT-OUTPUT STABILI
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168 but sup lH(.7w)I W CHAPTER 6. I
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184 CHAPTER 7. INPUT-TO-STATE STABI
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CHAPTER 7. INPUT-TO-STATE STABILITY
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Chapter 8 Passivity The objective o
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8.1. POWER AND ENERGY: PASSIVE SYST
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8.2. DEFINITIONS 205 Example 8.1 Le
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8.2. DEFINITIONS 207 Definition 8.4
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3.3. INTERCONNECTIONS OF PASSIVITY
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8.4. STABILITY OF FEEDBACK INTERCON
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8.4. STABILITY OF FEEDBACK INTERCON
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8.5. PASSIVITY OF LINEAR TIME-INVAR
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8.6. STRICTLY POSITIVE REAL RATIONA
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8.6. STRICTLY POSITIVE REAL RATIONA
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8.7. EXERCISES 221 Notes and Refere
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224 CHAPTER 9. DISSIPATIVITY theory
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226 CHAPTER 9. DISSIPATWITY Inequal
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228 CHAPTER 9. DISSIPATIVITY Thus,
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230 CHAPTER 9. DISSIPATWITY Figure
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232 CHAPTER 9. DISSIPATIVITY As def
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234 CHAPTER 9. DISSIPATIVITY for al
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236 CHAPTER 9. DISSIPATIVITY which
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238 CHAPTER 9. DISSIPATIVITY proper
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240 CHAPTER 9. DISSIPATIVITY Figure
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242 CHAPTER 9. DISSIPATIVITY Thus b
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244 CHAPTER 9. DISSIPATWITY This re
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246 CHAPTER 9. DISSIPATIVITY Thus,
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248 CHAPTER 9. DISSIPATIVITY d G u
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250 CHAPTER 9. DISSIPATIVITY U I I
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252 CHAPTER 9. DISSIPATIVITY x = a(
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254 CHAPTER 9. DISSIPATIVITY (9.5)
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256 CHAPTER 10. FEEDBACK LINEARIZAT
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Chapter 11 Nonlinear Observers So f
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11.1. OBSERVERS FOR LINEAR TIME-INV
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11.1. OBSERVERS FOR LINEAR TIME-INV
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11.2. NONLINEAR OBSERVABILITY 297 T
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11.3. OBSERVERS WITH LINEAR ERROR D
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11.4. LIPSCHITZ SYSTEMS 301 11.4 Li
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11.5. NONLINEAR SEPARATION PRINCIPL
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11.5. NONLINEAR SEPARATION PRINCIPL
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Appendix A Proofs The purpose of th
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A.1. CHAPTER 3 309 Figure A.2: Asym
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A.1. CHAPTER 3 is symmetric. Proof:
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A.2. CHAPTER 4 313 Lemma 3.5: The p
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itrJ A.3. CHAPTER 6 V 315 Thus, f I
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A.3. CHAPTER 6 317 It follows that
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A.3. CHAPTER 6 319 Condition (ii):
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A.4. CHAPTER 7 321 and av ax < ki l
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A.4. CHAPTER 7 323 With this proper
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A.5. CHAPTER 8 325 (b) : Assume fir
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A.5. CHAPTER 8 327 H1 :............
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A.6. CHAPTER 9 329 that is ff ffo T
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A. 7. CHAPTER 10 331 Equations (A.6
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A.7. CHAPTER 10 333 (i) j = 0: For
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A.7. CHAPTER 10 335 Proof of Theore
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338 BIBLIOGRAPHY [12] R. W. Brocket
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340 BIBLIOGRAPHY [43] P. Kokotovic,
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342 BIBLIOGRAPHY [72] E. D. Sontag,
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List of Figures 1.1 mass-spring sys
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LIST OF FIGURES 347 6.12 The nonlin
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350 globally uniformly asymptotical
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352 Subspaces, 36 Supply rate, 224
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