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Finite-Time Stability and H ∞ Control of Linear Discrete-Time Delay Systems with Norm-Bounded Disturbances

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Abstract

This paper deals with the finite-time stability and H ∞ control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First, new sufficient conditions are established for robust finite-time stability of the linear discrete-time delay system with norm-bounded disturbances, then the state feedback controller is designed to robustly finite-time stabilize the system and guarantee an adequate level of system performance. The delay-dependent sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed results.

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Acknowledgments

This work was completed when the second author was visiting the Vietnam Institute for Advance Study in Mathematics (VIASM). He would like to gratefully acknowledge VIASM for the support and hospitality. This work was supported by the National Foundation for Science and Technology Development of Vietnam (NAFOSTED- grant 101.01-2014.35). The authors also thank anonymous referees for their valuable comments and suggestions, which allowed us them to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Hue University, Hue, Vietnam

    Le A. Tuan

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

    Vu N. Phat

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  1. Le A. Tuan
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  2. Vu N. Phat
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Correspondence to Vu N. Phat.

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Tuan, L.A., Phat, V.N. Finite-Time Stability and H ∞ Control of Linear Discrete-Time Delay Systems with Norm-Bounded Disturbances. Acta Math Vietnam 41, 481–493 (2016). https://doi.org/10.1007/s40306-015-0155-7

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  • DOI: https://doi.org/10.1007/s40306-015-0155-7

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