ESSENTIALS OF 目 ROBUST E CONTROLI e11n∠101 WITH JOHN C. DOYLE PRENTICE HALL
ESSENTIALS OF ROBUST CONTROL Kemin Zhou May25,1999
ESSENTIALS OF ROBUST CONTROL Kemin Zhou May 25, 1999
Preface Robustness of control systems to disturbances and uncertainties has always been the central issue in feedback control. Feedback would not be needed for most control systems if there were no disturbances and uncertainties. Developing multivariable robust control methods has been the focal point in the last two decades in the control community. The state-of-the-art Hoo robust control theory is the result of this effort. another book by this author, John C. Doyle, and Keith Glover, entitled Robust and Optimal Control, which has been extensively class-tested in many universities around the world. Unlike that book, which is intended primarily as a comprehensive reference of robust and Hoo control theory, this book is intended to be a text for a graduate course in multivariable control. It is also intended to be a reference for practicing control engineers who are interested in applying the state-of-the-art robust control techniques in their applications. With this objective in mind, I have streamlined the presentation added more than 50 illustrative examples, included many related MATLAB commands and more than 150 exercise problems, and added some recent developments in the area of robust control such as gap metric, v-gap metric, model validation, and mixed u problem. In addition, many proofs are os completely rewritten and some advanced topics are either deleted completely or do not get an in-depth treatment The prerequisite for reading this book is some basic knowledge of classical control theory and state-space theory. The text contains more material than could be covered in detail in a one-semester or a one-quarter course. Chapter 1 gives a chapter-by-chapter summary of the main results presented in the book, which could be used as a guide for the selection of topics for a specific course. Chapters 2 and 3 can be used as a refresher for some linear algebra facts and some standard linear system theory. A course focusing on Hoo control should cover at least most parts of Chapters 4-6, 8, 9, 11-13, and Sections 14.1 and 14.2. An advanced Hoo control course should also include the rest of Chapter 14, Chapter 16, and possibly Chapters 10, 7, and 15. A course focusing on robustness and model uncertainty should cover at least Chapters 4, 5, and 8-10. Chapters 17 and 18 can be added to any advanced robust and Hoo control course if time permits I have tried hard to eliminate obvious mistakes. It is, however, impossible for me to make the book perfect. Readers are encouraged to send corrections, comments, and MATLAB is a registered trademark of The Math Works, Inc
Preface Robustness of control systems to disturbances and uncertainties has always been the central issue in feedback control. Feedback would not be needed for most control systems if there were no disturbances and uncertainties. Developing multivariable robust control methods has been the focal point in the last two decades in the control community. The state-of-the-art H∞ robust control theory is the result of this effort. This book introduces some essentials of robust and H∞ control theory. It grew from another book by this author, John C. Doyle, and Keith Glover, entitled Robust and Optimal Control, which has been extensively class-tested in many universities around the world. Unlike that book, which is intended primarily as a comprehensive reference of robust and H∞ control theory, this book is intended to be a text for a graduate course in multivariable control. It is also intended to be a reference for practicing control engineers who are interested in applying the state-of-the-art robust control techniques in their applications. With this objective in mind, I have streamlined the presentation, added more than 50 illustrative examples, included many related Matlab R commands1 and more than 150 exercise problems, and added some recent developments in the area of robust control such as gap metric, ν-gap metric, model validation, and mixed µ problem. In addition, many proofs are completely rewritten and some advanced topics are either deleted completely or do not get an in-depth treatment. The prerequisite for reading this book is some basic knowledge of classical control theory and state-space theory. The text contains more material than could be covered in detail in a one-semester or a one-quarter course. Chapter 1 gives a chapter-by-chapter summary of the main results presented in the book, which could be used as a guide for the selection of topics for a specific course. Chapters 2 and 3 can be used as a refresher for some linear algebra facts and some standard linear system theory. A course focusing on H∞ control should cover at least most parts of Chapters 4–6, 8, 9, 11–13, and Sections 14.1 and 14.2. An advanced H∞ control course should also include the rest of Chapter 14, Chapter 16, and possibly Chapters 10, 7, and 15. A course focusing on robustness and model uncertainty should cover at least Chapters 4, 5, and 8–10. Chapters 17 and 18 can be added to any advanced robust and H∞ control course if time permits. I have tried hard to eliminate obvious mistakes. It is, however, impossible for me to make the book perfect. Readers are encouraged to send corrections, comments, and 1Matlab is a registered trademark of The MathWorks, Inc. vii
PREFACE suggestions to me, preferably by electronic mail, at kemin@ee. Isu. edu I am also planning to put any corrections, modifications, and extensions on the Internet so that they can be obtained either from the following anonymous ftp ftp gate. ee. lsu. edu cd pub/kemin/books/ essentials or from the author's home page http://kilo.ee.lsuedu/kemin/books/essentials/ This book would not be possible without the work done jointly for the previous book with Professor John C. Doyle and Professor Keith Glover. I thank them for their influence on my research and on this book. Their serious attitudes toward scientific research have been reference models for me. I am especially grateful to John for having me as a research fellow in Caltech, where I had two very enjoyable years and had opportunities to catch a glimpse of his"BIG PICTURE of control I want to thank my editor from Prentice Hall, Tom Robbins, who originally proposed he idea for this book and has been a constant source of support for me while writing it Without his support and encouragement, this project would have been a difficult one It has been my great pleasure to work with him. I would like to express my sincere gratitude to Professor Bruce A. Francis for giving me many helpful comments and suggestions on this book. Professor Francis has also kindly provided many exercises in the book. I am also grateful to Professor Kang-Zhi liu and Professor Zheng-Hua Luo, who have made many useful comments and suggestions I want to thank Professor Glen Vinnicombe for his generous help in the preparation of Chapters 16 and 17. Special thanks go to Professor Jianqing Mao for providing me the opportunity to present much of this material in a series of lectures at Beijing University of aeronautics and astronautics in the summer of 1996 In addition, I would like to thank all those who have helped in many ways in making this book possible, especially Professor Pramod P Khargonekar, Professor Andre Tit Professor Andrew Packard, Professor Jie Chen, Professor Jakob Stoustrup, Professor Hans Henrik Niemann, Professor Malcolm Smith, Professor Tryphon Georgiou, Profes- sor Tongwen Chen, Professor Hitay Ozbay, Professor Gary Balas, Professor Carolyn Beck, Professor Dennis S Bernstein, Professor Mohamed Darouach, Dr. Bobby Boden- heimer, Professor Guoxiang Gu, Dr. Weimin Lu, Dr. John Morris, Dr. Matt Newlin Professor Li Qiu, Professor Hector P. Rotstein, Professor Andrew Teel, Professor Ja- gannathan Ramanujam, Dr. Linda G. Bushnell, Xiang Chen, Greg Salomon, Pablo A Parrilo, and many other people for supporting my research: National Air Force of scientific Research. and the board of regents in the state of louisiana nally, I would like to thank my wife, Jing, and my son, Eric, for their generous support, understanding, and patience during the writing of this book Kemin zhou
viii PREFACE suggestions to me, preferably by electronic mail, at kemin@ee.lsu.edu I am also planning to put any corrections, modifications, and extensions on the Internet so that they can be obtained either from the following anonymous ftp: ftp gate.ee.lsu.edu cd pub/kemin/books/essentials/ or from the author’s home page: http://kilo.ee.lsu.edu/kemin/books/essentials/ This book would not be possible without the work done jointly for the previous book with Professor John C. Doyle and Professor Keith Glover. I thank them for their influence on my research and on this book. Their serious attitudes toward scientific research have been reference models for me. I am especially grateful to John for having me as a research fellow in Caltech, where I had two very enjoyable years and had opportunities to catch a glimpse of his “BIG PICTURE” of control. I want to thank my editor from Prentice Hall, Tom Robbins, who originally proposed the idea for this book and has been a constant source of support for me while writing it. Without his support and encouragement, this project would have been a difficult one. It has been my great pleasure to work with him. I would like to express my sincere gratitude to Professor Bruce A. Francis for giving me many helpful comments and suggestions on this book. Professor Francis has also kindly provided many exercises in the book. I am also grateful to Professor Kang-Zhi Liu and Professor Zheng-Hua Luo, who have made many useful comments and suggestions. I want to thank Professor Glen Vinnicombe for his generous help in the preparation of Chapters 16 and 17. Special thanks go to Professor Jianqing Mao for providing me the opportunity to present much of this material in a series of lectures at Beijing University of Aeronautics and Astronautics in the summer of 1996. In addition, I would like to thank all those who have helped in many ways in making this book possible, especially Professor Pramod P. Khargonekar, Professor Andr´e Tits, Professor Andrew Packard, Professor Jie Chen, Professor Jakob Stoustrup, Professor Hans Henrik Niemann, Professor Malcolm Smith, Professor Tryphon Georgiou, Professor Tongwen Chen, Professor Hitay Ozbay, Professor Gary Balas, Professor Carolyn ¨ Beck, Professor Dennis S. Bernstein, Professor Mohamed Darouach, Dr. Bobby Bodenheimer, Professor Guoxiang Gu, Dr. Weimin Lu, Dr. John Morris, Dr. Matt Newlin, Professor Li Qiu, Professor Hector P. Rotstein, Professor Andrew Teel, Professor Jagannathan Ramanujam, Dr. Linda G. Bushnell, Xiang Chen, Greg Salomon, Pablo A. Parrilo, and many other people. I would also like to thank the following agencies for supporting my research: National Science Foundation, Army Research Office (ARO), Air Force of Scientific Research, and the Board of Regents in the State of Louisiana. Finally, I would like to thank my wife, Jing, and my son, Eric, for their generous support, understanding, and patience during the writing of this book. Kemin Zhou
PREFACE Here is how Hoo is pronounced in Chi 愛趣無窮 It means "The joy of love is endless
PREFACE ix Here is how H∞ is pronounced in Chinese: It means “The joy of love is endless