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Research Papers

Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems

[+] Author and Article Information
Wenping Xue

Institute of Cyber-Systems and Control,
Zhejiang University,
Hangzhou 310027, China;
School of Electrical and Information Engineering,
Jiangsu University, Zhenjiang 212013, China
e-mail: xwping@zju.edu.cn

Weijie Mao

Institute of Cyber-Systems and Control,
Zhejiang University,
Hangzhou 310027, China
e-mail: wjmao@iipc.zju.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received May 3, 2012; final manuscript received December 6, 2012; published online March 28, 2013. Assoc. Editor: Bor-Chin Chang.

J. Dyn. Sys., Meas., Control 135(3), 031018 (Mar 28, 2013) (6 pages) Paper No: DS-12-1127; doi: 10.1115/1.4023213 History: Received May 03, 2012; Revised December 06, 2012

The problems of admissible finite-time stability (AFTS) and admissible finite-time stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is admissibly finite-time stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.

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