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Stability and Stabilization of Linear and Fuzzy Time-Delay Systems pp 33–123Cite as

Stability Analysis of Time-Delay Systems

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 141))

Abstract

This chapter deals with the stability analysis of linear time-delay systems without and with parametric uncertainties. The stability analysis for both constant and time-varying delay in the states is considered. The focus of this chapter is to review the existing methods on delay-dependent stability analysis in an LMI framework based on Lyapunov-Krasovskii approach and consequently the improved results on delay-dependent stability analysis are presented. The results of the proposed techniques are validated by considering numerical examples and compared with existing results.

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Notes

  1. 1.

    \(A(t)=A+\Delta A(t)\), where, \(\Delta A(t)=D_{a}F_{a}(t)E_{a}\).

  2. 2.

    \(A_{d}(t)=A+\Delta A_{d}(t)\), where, \(\Delta A_{d}(t)=D_{d}F_{d}(t)E_{d}\).

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Author information

Authors and Affiliations

  1. National Institute of Technology Silchar, Silchar, Assam, India

    Rajeeb Dey

  2. Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India

    Goshaidas Ray

  3. “Aurel Vlaicu” University of Arad, Arad, Romania

    Valentina Emilia Balas

Authors
  1. Rajeeb Dey
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  2. Goshaidas Ray
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  3. Valentina Emilia Balas
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Correspondence to Rajeeb Dey .

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Dey, R., Ray, G., Balas, V.E. (2018). Stability Analysis of Time-Delay Systems. In: Stability and Stabilization of Linear and Fuzzy Time-Delay Systems. Intelligent Systems Reference Library, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-70149-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-70149-3_2

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