Holdings: Piecewise linear control systems

Piecewise linear control systems: a computational approach

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Bibliographic Details
Main Author:	Johansson, Mikael (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2003
Series:	Lecture notes in control and information sciences 284
Subjects:	Commande linéaire Topologie linéaire par morceaux Linear control systems Piecewise linear topology Lineares Regelungssystem Dynamisches System Ljapunov-Stabilitätstheorie Hybrides System Fuzzy-Regelung Reglerentwurf
Online Access:	Inhaltsverzeichnis
Physical Description:	202 S. Ill., graph. Darst.
ISBN:	3540441247

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Record in the Search Index

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adam_text	CONTENTS 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. PIECEWISE LINEAR MODELING . . . . . . . . . . . . . . . . . . . . . 9 2.1 MODEL REPRESENTATION . . . . . . . . . . . . . . . . . . . . . 9 2.2 SOLUTION CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . 1 4 2.3 UNCERTAINTY MODELS . . . . . . . . . . . . . . . . . . . . . . 21 2.4 MODULARITY AND INTERCONNECTIONS . . . . . . . . . . . . . . 26 2.5 PIECEWISE LINEAR FUNCTION REPRESENTATIONS . . . . . . . . . 28 2.6 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 30 3. STRUCTURAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1 EQUILIBRIUM POINTS AND THE STEADY-STATE CHARACTERISTIC . . 32 3.2 CONSTRAINT VERIFICATION AND INVARIANCE . . . . . . . . . . . 35 3.3 DETECTING ATTRACTIVE SLIDING MODES ON CELL BOUNDARIES . 37 3.4 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 39 4. LYAPUNOV STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1 EXPONENTIAL STABILITY . . . . . . . . . . . . . . . . . . . . . . 41 4.2 QUADRATIC STABILITY . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 CONSERVATISM OF QUADRATIC STABILITY . . . . . . . . . . . . . 4 6 4.4 FROM QUADRATIC TO PIECEWISE QUADRATIC . . . . . . . . . . . 48 4.5 INTERLUDE: DESCRIBING PARTITION PROPERTIES . . . . . . . . . 51 4.6 PIECEWISE QUADRATIC LYAPUNOV FUNCTIONS . . . . . . . . . 55 4.7 ANALYSIS OF PIECEWISE LINEAR DIFFERENTIAL INCLUSIONS . . . . 61 4.8 ANALYSIS OF SYSTEMS WITH ATTRACTIVE SLIDING MODES . . . . 63 4.9 IMPROVING COMPUTATIONAL EFFICIENCY . . . . . . . . . . . . 66 4.10 PIECEWISE LINEAR LYAPUNOV FUNCTIONS . . . . . . . . . . . 72 4.11 A UNIFYING VIEW . . . . . . . . . . . . . . . . . . . . . . . . 77 4.12 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 82 5. DISSIPATIVITY ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 85 5.1 DISSIPATIVITY ANALYSIS VIA CONVEX OPTIMIZATION . . . . . . 86 CONTENTS 5.2 COMPUTATION OF L 2 -INDUCED GAIN . . . . . . . . . . . . . . 88 5.3 ESTIMATION OF TRANSIENT ENERGY . . . . . . . . . . . . . . . . 89 5.4 DISSIPATIVE SYSTEMS WITH QUADRATIC SUPPLY RATES . . . . . 91 5.5 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 95 6. CONTROLLER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.1 QUADRATIC STABILIZATION OF PIECEWISE LINEAR SYSTEMS . . . 9 7 6.2 CONTROLLER SYNTHESIS BASED ON PIECEWISE QUADRATICS . . . 9 8 6.3 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 105 7. SELECTED TOPICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.1 ESTIMATION OF REGIONS OF ATTRACTION . . . . . . . . . . . . . 108 7.2 RIGOROUS ANALYSIS OF SMOOTH NONLINEAR SYSTEMS . . . . . 115 7.3 AUTOMATED PARTITION REFINEMENTS . . . . . . . . . . . . . . 117 7.4 FUZZY LOGIC SYSTEMS . . . . . . . . . . . . . . . . . . . . . 120 7.5 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 126 8. LINEAR HYBRID DYNAMICAL SYSTEMS . . . . . . . . . . . . . . . . . 129 8.1 LINEAR HYBRID DYNAMICAL SYSTEMS . . . . . . . . . . . . . 130 8.2 ANALYSIS USING DISCONTINUOUS LYAPUNOV FUNCTIONS . . . . 132 8.3 STABILITY ANALYSIS USING LYAPUNOV FUNCTIONALS . . . . . . 135 8.4 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 139 9. CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . 142 A. COMPUTATIONAL ISSUES . . . . . . . . . . . . . . . . . . . . . . . . . 144 A.1 LINEAR AND SEMIDEFINITE PROGRAMMING . . . . . . . . . . . 145 A.2 POLYHEDRA, POLYTOPES, AND ELLIPSOIDS . . . . . . . . . . . . 148 A.3 POLYHEDRAL PARTITIONS . . . . . . . . . . . . . . . . . . . . . 157 A.4 CONSTRAINT MATRICES . . . . . . . . . . . . . . . . . . . . . . 159 A.5 ON THE S-PROCEDURE I NPIECEWISE QUADRATIC ANALYSIS . . . 165 A.6 COMMENTS AND REFERENCES . . . . . . . . . . . . . . . . . . 170 B. PROOFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 B.1 PROOFS FROM CHAPTER 2 . . . . . . . . . . . . . . . . . . . . . 171 B.2 PROOFS FROM CHAPTER 4 . . . . . . . . . . . . . . . . . . . . . 172 B.3 PROOFS FROM CHAPTER 5 . . . . . . . . . . . . . . . . . . . . . 177 B.4 PROOFS FROM CHAPTER 6 . . . . . . . . . . . . . . . . . . . . . 178 B.5 PROOFS FROM CHAPTER 7 . . . . . . . . . . . . . . . . . . . . . 179 B.6 PROOFS FROM CHAPTER A . . . . . . . . . . . . . . . . . . . . 180 C. BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
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author	Johansson, Mikael
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discipline	Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik
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spelling	Johansson, Mikael Verfasser aut Piecewise linear control systems a computational approach Mikael Johansson Berlin [u.a.] Springer 2003 202 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 284 Engineering online library Commande linéaire Topologie linéaire par morceaux Linear control systems Piecewise linear topology Lineares Regelungssystem (DE-588)4167730-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Hybrides System (DE-588)4510314-8 gnd rswk-swf Fuzzy-Regelung (DE-588)4395755-9 gnd rswk-swf Reglerentwurf (DE-588)4177447-4 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 s Reglerentwurf (DE-588)4177447-4 s Fuzzy-Regelung (DE-588)4395755-9 s Hybrides System (DE-588)4510314-8 s Dynamisches System (DE-588)4013396-5 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Lecture notes in control and information sciences 284 (DE-604)BV005848579 284 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009959970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Johansson, Mikael Piecewise linear control systems a computational approach Lecture notes in control and information sciences Commande linéaire Topologie linéaire par morceaux Linear control systems Piecewise linear topology Lineares Regelungssystem (DE-588)4167730-4 gnd Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Hybrides System (DE-588)4510314-8 gnd Fuzzy-Regelung (DE-588)4395755-9 gnd Reglerentwurf (DE-588)4177447-4 gnd
subject_GND	(DE-588)4167730-4 (DE-588)4013396-5 (DE-588)4167992-1 (DE-588)4510314-8 (DE-588)4395755-9 (DE-588)4177447-4
title	Piecewise linear control systems a computational approach
title_auth	Piecewise linear control systems a computational approach
title_exact_search	Piecewise linear control systems a computational approach
title_full	Piecewise linear control systems a computational approach Mikael Johansson
title_fullStr	Piecewise linear control systems a computational approach Mikael Johansson
title_full_unstemmed	Piecewise linear control systems a computational approach Mikael Johansson
title_short	Piecewise linear control systems
title_sort	piecewise linear control systems a computational approach
title_sub	a computational approach
topic	Commande linéaire Topologie linéaire par morceaux Linear control systems Piecewise linear topology Lineares Regelungssystem (DE-588)4167730-4 gnd Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Hybrides System (DE-588)4510314-8 gnd Fuzzy-Regelung (DE-588)4395755-9 gnd Reglerentwurf (DE-588)4177447-4 gnd
topic_facet	Commande linéaire Topologie linéaire par morceaux Linear control systems Piecewise linear topology Lineares Regelungssystem Dynamisches System Ljapunov-Stabilitätstheorie Hybrides System Fuzzy-Regelung Reglerentwurf
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volume_link	(DE-604)BV005848579
work_keys_str_mv	AT johanssonmikael piecewiselinearcontrolsystemsacomputationalapproach

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