LMIs in Control Systems: Analysis, Design and Applications

Although LMI has emerged as a powerful tool with applications across the major domains of systems and control, there has been a need for a textbook that provides an accessible introduction to LMIs in control systems analysis and design. Filling this need, LMIs in Control Systems: Analysis, Design and Applications focuses on the basic analysis and design problems of both continuous- and discrete-time linear systems based on LMI methods.

Providing a broad and systematic introduction to the rich content of LMI-based control systems analysis and design with applications, this book is suitable for use as a textbook for LMI related courses for senior undergraduate and postgraduate students in the fields of control systems theory and applications.

Key Features:

• Contains four well-structured parts: Preliminaries, Control Systems Analysis, Control Systems Design, and Applications, as well as an introduction chapter and two appendices
• Summarizes most of the technical lemmas used in the book in one preliminary chapter, and classifies them systematically into different groups
• Includes many examples, exercises, and practical application backgrounds
• Summarizes most of the important results in the last section of each chapter, in a clear table format
• Contains an application part composed of two chapters that respectively deal with missile and satellite attitude control using LMI techniques
• Provides a brief and clear introduction to the use of the LMI Lab in the MATLAB® Robust Control Toolbox
• Supplies detailed proofs for all main results, with lengthy ones clearly divided into different subsections or steps―using elementary mathematics whenever possible
• Uses a pole assignment Benchmark problem, in support of the numerical reliability of LMI techniques, where numerical unreliability could result in a solution to a problem that is far from the true one

A Solutions Manual and MATLAB® codes for the computational exercise problems and examples are available upon qualified course adoption.

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.