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.
Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems
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.
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Xue, W., and Mao, W. (March 28, 2013). "Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems." ASME. J. Dyn. Sys., Meas., Control. May 2013; 135(3): 031018. https://doi.org/10.1115/1.4023213
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