LMI-based robust admissible control for uncertain singular delta operator systems

Abstract

This paper investigates the problem of state feedback robust admissible control for singular delta operator systems with norm-bounded coefficient matrix uncertainties. A necessary and sufficient condition is derived to ensure the admissibility of the closed-loop singular delta operator system for all allowable uncertainties. Then, by specifying the structure of some matrix variables, the existence condition and explicit expression of a robust admissible controller are obtained in terms of strict linear matrix inequalities. Moreover, from the relation between singular discrete systems and singular delta operator systems, the corresponding results are also presented for uncertain singular discrete systems. Finally, some numerical examples are provided to demonstrate the effectiveness of the results in this paper.

Keywords:

• singular delta operator systems
• norm-bounded uncertainties
• robust admissible control
• state feedback
• LMI

Acknowledgements

The author would like to thank the associate editor and the anonymous reviewers for the valuable and helpful comments and suggestions which helped to improve the quality of the paper greatly.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61104001].

Notes on contributors

Xin-Zhuang Dong

Xin-Zhuang Dong received her B.Sc. degree in applied mathematics from the Institute of Information Engineering of People’s Liberation Army (PLA), China, in 1994, M.Sc. degree from the Institute of Electronic Technology of PLA, China, in 1998, and Ph.D. degree in control theory and control engineering from Northeastern University, China, in 2004. From 2004 to 2006, she was a postdoctoral researcher in the Academy of Mathematics and Systems Science, Chinese Academy of Science. Since August 2006, she has been affiliated with the College of Automation Engineering, Qingdao University. She is an associate professor in the Department of Control Engineering. Her research interests include singular system theory, robust control, sliding mode control and DOSs.