LMIs in Control Systems

Linear matrix inequalities (LMIs) have emerged as a powerful tool which has found numerous applications in many major domains of systems control, and it's getting more and more popular. This book provides a relatively systematic introduction to the basic results in LMI-based control systems analysis and design. Designed as a textbook for certain graduate and senior undergraduate courses in control systems analysis and design, it focuses on the analysis and design problems on both continuous- and discrete-time linear systems based on the LMI methods.

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.

Introduction. Preliminaries. Technical Lemmas. Review of Optimization Theory. Control Systems Analysis. Stability Analysis. H-/H2 Performance. Property Analysis. Control Systems Design. Feedback Stabilization. H-/H2 Control. State Observation and Filtering. Multiple Objective Designs. Applications. Missile Attitude Control. Satellite Control. Appendices.