Slotine • Li APPLIED NONLINEAR CONTROL

1 Slotine Li APPLIED NONLINEAR CONTROL ! iAPPLIEDNONLINEARCONTROLJean-Jacques E SlotineWeiping LiAppliedNonlinearControlJEAN-JACQUES E. SLOTINEM assachusetts Institute of TechnologyWEIPING LIMassachusetts Institute of Technology'Prentice HallEnglewood Cliffs, New Jersey 07632 Library of Congress Cataloging-in-Publication DataSlotine, E. (Jean-Jacques E.) APPLIED NONLINEAR CONTROL / Jean-Jacques E. Slotine , Weiping Lip. bibliographical 0-13-040890-51, NONLINEAR CONTROL theory. I. Li, Weiping. II. 1991 '312-dc20 C1 PEditorial/production supervision andinterior design: JENNIFER WENZELC over design: KAREN STEPHENSM anufacturing Buyer: LORI BULWIN=^= 1991 by Prentice-Hall, Inc.

2 ^=&= A Division of Simon & SchusterT k Englewood Cliffs, New Jersey 07632 All rights reserved. No part of this book may bereproduced, in any form or by any means,without permission in writing from the in the United States of America20 19 18 17 16 15 14 13 12 1]ISBN D-13-DHDfiTa-SPrentice-Hall International (UK) Limited, LondonPrentice-Hall of Australia Pty. Limited, SydneyPrentice-Hall Canada Inc., TorontoPrentice-Hail Hispanoamericana, , MexicoPrentice-Hall of India Private Limited, New DelhiPrentice-Hall of Japan, Inc., TokyoSimon & Schuster Asia Pte. Ltd., SingaporeEditora Prentice-Hall do Brasil, Ltda., Rio de JaneiroTo Our ParentsContentsPreface xi1.

3 Introduction Why NONLINEAR CONTROL ? NONLINEAR System Behavior An Overview of the Book Notes and References 13 Part I: NONLINEAR Systems analysis 14 Introduction to Part I 142. Phase Plane analysis Concepts of Phase Plane analysis Phase Portraits Singular Points Symmetry in Phase Plane Portraits Constructing Phase Portraits Determining Time from Phase Portraits Phase Plane analysis of Linear Systems Phase Plane analysis of NONLINEAR Systems Existence of Limit Cycles

4 Summary Notes and References Exercises 38VI113. Fundamentals of Lyapunov Theory NONLINEAR Systems and Equilibrium Points Concepts of Stability Linearization and Local Stability Lyapunov's Direct Method Positive Definite Functions and Lyapunov Functions Equilibrium Point Theorems Invariant Set Theorems System analysis Based on Lyapunov's Direct Method Lyapunov analysis of Linear Time-Invariant Systems

5 Krasovskii's Method The Variable Gradient Method Physically Motivated Lyapunov Functions Performance analysis CONTROL Design Based on Lyapunov's Direct Method Summary Notes and References Exercises 974. Advanced Stability Theory Concepts of Stability for Non-Autonomous Systems Lyapunov analysis of Non-Autonomous Systems Lyapunov's Direct Method for Non-Autonomous Systems Lyapunov analysis of Linear Time-Varying Systems The Linearization Method for Non-Autonomous Systems * Instability Theorems * Existence of Lyapunov Functions Lyapunov-Like analysis Using Barbalat's Lemma Asymptotic Properties of

6 Functions and Their Derivatives Barbalat's Lemma Positive Linear Systems PR and SPR Transfer Functions The Kalman-Yakubovich Lemma Positive Real Transfer Matrices The Passivity Formalism Block Combinations Passivity in Linear Systems * Absolute Stability * Establishing Boundedness of Signals * Existence and Unicity of Solutions Summary Notes and References Exercises 1545.

7 Describing Function analysis Describing Function Fundamentals An Example of Describing Function analysis Applications Domain Basic Assumptions Basic Definitions Computing Describing Functions Common Nonlinearities In CONTROL Systems Describing Functions of Common Nonlinearities Describing Function analysis of NONLINEAR Systems The Nyquist Criterion and Its Extension Existence of Limit Cycles Stability of Limit Cycles Reliability of Describing Function analysis Summary Notes and References Exercises 188 Part II: NONLINEAR CONTROL Systems Design 191 Introduction to Part II 1916.

8 Feedback Linearization Intuitive Concepts Feedback Linearization And The Canonical Form Input-State Linearization Input-Output Linearization Mathematical Tools Input-State Linearization of SISO Systems Input-Output Linearization of SISO Systems * Multi-Input Systems Summary Notes and References Exercises 2717.

9 Sliding CONTROL Sliding Surfaces A Notational Simplification * Filippov's Construction of the Equivalent Dynamics Perfect Performance - At a Price Direct Implementations of Switching CONTROL Laws Continuous Approximations of Switching CONTROL Laws The Modeling/Performance Trade-Offs * Multi-Input Systems Summary Notes and References Exercises 3078.

10 Adaptive CONTROL Basic Concepts in Adaptive CONTROL Why Adaptive CONTROL ? What Is Adaptive CONTROL ? How To Design Adaptive Controllers ? Adaptive CONTROL of First-Order Systems Adaptive CONTROL of Linear Systems With Full State Feedback Adaptive CONTROL of Linear Systems With Output Feedback Linear Systems With Relative Degree One Linear Systems With Higher Relative Degree Adaptive CONTROL of NONLINEAR Systems Robustness of Adaptive CONTROL Systems * On-Line Parameter Estimation Linear Parametrization Model