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Stability Analysis for Linear Systems with Time-Varying Delay

In: Dynamic Systems with Time Delays: Stability and Control

Author

Listed:
  • Ju H. Park

    (Yeungnam University, Department of Electrical Engineering)

  • Tae H. Lee

    (Chonbuk National University, Division of Electronic Engineering)

  • Yajuan Liu

    (North China Electric Power University, Control and Computer Engineering)

  • Jun Chen

    (Jiangsu Normal University, School of Electrical Engineering and Automation)

Abstract

This chapter is concerned with the stability problem for linear systems with a time-varying delay by using the Lyapunov–Krasovskii (L–K) functionalLyapunov–Krasovskii functional method. Integral/summation inequalities proposed in the previous chapters are utilized and corresponding L–K functionals are deliberately constructed. According to the ways of estimating the single-integral/summation term arising in the derivative or the forward difference of L–K functionals, two types of stability conditions are consequently obtained: those obtained by the combination of integral/summation inequalities without free matrices and the reciprocally convex lemma and those obtained by integral/summation inequalities with free matrices. The relationship between them is closely studied. It is pointed out that the conservatism of the two types of corresponding conditions cannot be compared in theory.

Suggested Citation

  • Ju H. Park & Tae H. Lee & Yajuan Liu & Jun Chen, 2019. "Stability Analysis for Linear Systems with Time-Varying Delay," Springer Books, in: Dynamic Systems with Time Delays: Stability and Control, chapter 5, pages 123-153, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-9254-2_5
    DOI: 10.1007/978-981-13-9254-2_5
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