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LMI Approach to Finite-Time Stability and Stabilization of Singular Linear Discrete Delay Systems

Acta Applicandae Mathematicae volume 146, pages 81–93 (2016)Cite this article

Abstract

This paper deals with finite-time stability and stabilization problem of singular linear discrete-time systems with time-varying delay and norm-bounded disturbance. We first present novel delay-dependent sufficient conditions for the robust finite-time stability of the system. Then the results are applied to solve finite-time stabilization problem of linear singular discrete-time control delay systems. The conditions are presented in terms of linear matrix inequalities, which can be determined by utilizing MATLABs LMI Control Toolbox. The effectiveness of the results are illustrated by numerical examples.

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Acknowledgements

This work was supported by the Thailand Research Fund (TRG5780203) and the National Foundation for Science and Technology Development, Vietnam under grant 101.01-2014.35. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which have improved our paper.

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Authors and Affiliations

  1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

    N. H. Muoi & V. N. Phat

  2. Department of Mathematics, Maejo University, Chiang Mai, 50290, Thailand

    G. Rajchakit

Authors
  1. N. H. Muoi
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  2. G. Rajchakit
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  3. V. N. Phat
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Correspondence to V. N. Phat.

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Muoi, N.H., Rajchakit, G. & Phat, V.N. LMI Approach to Finite-Time Stability and Stabilization of Singular Linear Discrete Delay Systems. Acta Appl Math 146, 81–93 (2016). https://doi.org/10.1007/s10440-016-0059-0

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  • DOI: https://doi.org/10.1007/s10440-016-0059-0

Keywords

  • Finite-time stability
  • Stabilization
  • Singular system
  • Time-varying delay
  • Disturbances
  • Linear matrix inequality