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International Journal of Systems Science

Volume 38, Issue 1, 2007

Dynamic output feedback H ∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach

Dynamic output feedback H control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach

DOI:
10.1080/00207720601042967
James Lama* & Shaosheng Zhoub

pages 25-37

Available online: 15 Mar 2007

Abstract

This article deals with an output feedback H control problem for a class of discrete-time fuzzy dynamic systems. A full-order dynamic output feedback H control design approach is developed by combining a fuzzy-basis-dependent Lyapunov function and a transformation on the controller parameters, which leads to sufficient conditions in the form of strict linear matrix inequalities (LMIs). The fuzzy-basis-dependent results are less conservative due to the generality of the fuzzy-basis-dependent Lyapunov function used which includes the fuzzy-basis-independent one as a special case. It has been shown that the underling full-order dynamic output feedback H control problem can be solved as LMI optimization problems that can be computed numerically very efficiently. Finally, two numerical examples, concerning the control of a discrete-time chaotic Lorenz system and an inverted pendulum, are given to demonstrate the applicability of the proposed approach.

Keywords

 

Details

  • Citation information:
  • Available online: 15 Mar 2007

Author affiliations

  • a Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
  • b Institute of Information and Control, School of Automation, Hangzhou Dianzi University, Hangzhou 310018, P.R. China

Author biographies

James Lam received a first class BSc degree in Mechanical Engineering from the University of Manchester in 1983. He was awarded the Ashbury Scholarship, the A.H. Gibson Prize and the H. Wright Baker Prize for his academic performance. From the University of Cambridge, he obtained the MPhil and PhD degrees in the area of control engineering in 1985 and 1988 respectively. His post-doctoral research was carried out in the Australian National University between 1990 and 1992. He is a Scholar and Fellow of the Croucher Foundation.

He is a Professor at the Department of Mechanical Engineering, the University of Hong Kong. Prior to that, he held faculty positions at the City University of Hong Kong and the University of Melbourne. He is holding a Guest Professorship at the Huazhong University of Science and Technology, Consulting Professorship at the South China University of Technology and Guest Professorship of Shandong University. Professor Lam is a Chartered Mathematician and Chartered Scientist, a Fellow of the Institute of Mathematics and its Applications, a Senior Member of the IEEE, a Member of the IEE. He is an Editor-in-Chief of the IEE Proceedings: Control Theory and Applications, an Associate Editor of the Asian Journal of Control, the International Journal of Systems Science, the Journal of Soundand Vibration, the Conference Editorial Board of the IEEE Control Systems Society, and on the editorial board of Journal of Applicable Functional Differential Equations. He has served on the IFAC Technical Committee on Control Design and the editorial board of the International Journal of Applied Mathematics and Computer Science. His research interests include model reduction, delay systems, descriptor systems, stochastic systems, multidimensional systems, robust control and filtering, fault detection and reliable control.

Shaosheng Zhou was born in Shandong, China, in 1965. He received the MSc degree in Applied Mathematics from Qufu Normal University in 1996, and the PhD degree in control theory and application from South-east University in 2001, respectively. He worked as a Research Associate in the Department of Manufacturing Engineering and Engineering management, the City University of Hong Kong from January 2000 to July 2000 and from November 2001 to June 2002. Frosm October 2002 to January 2003 and from November 2004 to April 2005, he worked as a Research Associate in the Department of Mechanical Engineering, the University of Hong Kong. He also worked as a research fellow in the School of Quantitative Methods and Mathematical Science, the University of Western Sydney from September 2005 to February 2006.

Dr. Zhou is currently a full professor at the Institute of Information and Control, School of Automation, Hangzhou Dianzi University and has co-authored more than 30 journal papers. His research interests are in nonlinear systems, robust control and filtering, time-delay systems, adaptive control and singular systems theory.

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