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Bessel-type inequality in semi-inner-product spaces and its application to stability analysis of discrete-time systems with distributed delays

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  • Huang, Yi-Bo
  • He, Yong

Abstract

In this paper, a Bessel-type inequality in semi-inner produce (s.i.p.) spaces is presented to deal with the problem of stability analysis for a class of discrete-time systems with distributed delays. The main purpose of this paper is to obtain less conservative stability conditions for the investigated systems. For this purpose, a novel inequality (which is referred to as Bessel-type inequality in s.i.p. spaces) is constructed by combining the Bessel inequality and a set of polynomials which is pairwise orthogonal in a s.i.p. space. The proposed inequality is more general than the conventional Jensen-type inequality, which is, to the best of our knowledge, the only inequality to deal with the problem of stability analysis for discrete-time systems with distributed delays up to now. Based on the proposed inequality and the Lyapunov-Krasovskii stability theory, a stability condition is presented. Finally, a numerical example is given to indicate that the proposed method is able to effectively reduce the conservatism.

Suggested Citation

  • Huang, Yi-Bo & He, Yong, 2022. "Bessel-type inequality in semi-inner-product spaces and its application to stability analysis of discrete-time systems with distributed delays," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002211
    DOI: 10.1016/j.amc.2022.127163
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    References listed on IDEAS

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    1. Zeng, Hong-Bing & Zhai, Zheng-Liang & He, Yong & Teo, Kok-Lay & Wang, Wei, 2020. "New insights on stability of sampled-data systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    2. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
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