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IMA Journal of Mathematical Control and Information Advance Access originally published online on October 28, 2005
IMA Journal of Mathematical Control and Information 2006 23(4):413-431; doi:10.1093/imamci/dni070
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Controllability and quadratic stability quadratic stabilization of discrete-time interval systems—an LMI approach

Da-Qing Zhang1,2, Qing-Ling Zhang3,** and Yue-Peng Chen3

1 Institute of System Science, Northeastern University, Shenyang Liaoning Province 110004, P. R. China, 2 College of Science, Anshan University of Science and Technology, Anshan Liaoning Province 114044, P. R. China, 3 Institute of System Science, Northeastern University, Shenyang Liaoning Province 110004, P. R. China

** Email: qlzhang{at}mail.neu.edu.cn


  Abstract

This paper presents necessary and sufficient conditions for discrete-time interval systems to be quadratically stable or quadratically stabilizable, and sufficient conditions for discrete-time interval systems to be controllable. All the results are obtained in terms of linear matrix inequality (LMI). With the LMI toolbox, the problems can be conveniently solved. Illustrative numerical examples show that the results are effective and less conservative to check the robust controllability and stability and to design the stabilizing controller for discrete-time interval systems.

Keywords: discrete interval systems; quadratic stability; quadratic stabilization; controllability; observability; linear matrix inequality (LMI).

Received on 14 December 2004. accepted on 25 May 2005.


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