LMIs in Control Systems ─ Analysis, Design and Applications

"Preface In recent years linear matrix inequalities (LMIs) have emerged as a powerful tool in the field of control systems analysis and design. Many problems such as state feedback synthesis, robustness analysis and design, H2 and H? control, can all be reduced to convex or quasi-convex problems that involve LMIs. The most attractive feature of LMIs lies in the fact that many problems in systems and control can be reduced to LMI problems, which can be solved both efficiently and numerical reliably. Very efficient algorithms to solve linear matrix inequalities have been developed and can be readily used through the mature Matlab LMI toolbox or the open source software packages YALMIP and CVX. LMIs today has been a real technique. With the help of the LMI techniques in control systems analysis and design, more and more theoretical and practical applications can now be solved, many of which might not be otherwise solved by traditional methods. Goal of the book The goal of this book is to provide a textbook for graduate and senior undergraduate courses in the field of control systems analysis and design, which contains the basic but systematic knowledge about LMIs and LMI-based control systems analysis and design. Boyd et al. (1994), which is the first book on LMIs, certainly has performed a pioneering function in the field, but limited by time it fails to catch up with the ever fast emerging new theories and techniques in LMIs. Yu (2002) is a book on LMI approach to robust control, which is suitable to be used as a textbook, but the Chinese language limits its usage worldwide"--

Guang-Ren Duan received his BSc. degree in Applied Mathematics, and both his MSc and PhD degrees in Control Systems Theory. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became full professor of control systems theory in the end of 1991. Prof. Duan visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998, and worked as a lecturer at the Queen's University of Belfast, UK from October 1998 to October 2002. Since August 2000, he has been elected Specially Employed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the Director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology.

He is the author and co-author of 3 books and more than 180 SCI indexed publications. Particularly, he has published with Springer a book entitled Analysis and Design of Descriptor Linear Systems, and has published over 30 papers in IEEE Transactions. His main research interests include parametric robust control systems design, LMI-based control systems analysis and design, descriptor systems, flight control and magnetic bearing control.

He has taught quite a few courses both at Harbin Institute of Technology, China, and at the Queen’s University of Belfast, UK. Particularly, he has lectured at Harbin Institute of Technology the graduate course "Linear Matrix Inequalities in Control Systems Analysis and Design", based on this set of lecture notes.