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An Equivalent Condition for Stability Analysis of LTI Systems with Bounded Time-invariant Delay

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  • Abolpour, Roozbeh
  • Khayatian, Alireza
  • Dehghani, Maryam
  • Rokhsari, Alireza

Abstract

This paper deals with the stability analysis of Linear Time-Invariant (LTI) systems in the presence of a bounded and time-invariant delay parameter. The paper extends the theory of characteristic quasi-polynomial to derive equivalent stability conditions. Based on the quasi-polynomial, a two-variate polynomial is defined and it is proved that system stability is equivalently guaranteed if all roots of the new polynomial are not allocated in a certain region of the right half plane (RHP). Moreover, the algorithm uses the proposed equivalent stability conditions to develop a set of implementable stability conditions based on the exposed edges theorem. The algorithm is applied to three simulation examples that admit some novel results for these systems. The first example shows the step-by-step procedure for the proposed algorithm. The second and the third ones compare various aspects of the proposed algorithm with some existing methods. Two hundred and fifty delay systems are randomly generated and the proposed algorithm is compared with them in terms of conservativeness and computational burden. The results reveal the superiority of the proposed method over the existing ones.

Suggested Citation

  • Abolpour, Roozbeh & Khayatian, Alireza & Dehghani, Maryam & Rokhsari, Alireza, 2023. "An Equivalent Condition for Stability Analysis of LTI Systems with Bounded Time-invariant Delay," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    • Handle: RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006580
    DOI: 10.1016/j.amc.2022.127585
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    References listed on IDEAS

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    1. Jorge-Antonio López-Renteria & Baltazar Aguirre-Hernández & Fernando Verduzco, 2011. "The Boundary Crossing Theorem and the Maximal Stability Interval," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-13, May.
    2. Roozbeh Abolpour & Maryam Dehghani & Heidar Ali Talebi, 2021. "A non-conservative state feedback control methodology for linear systems with state delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(12), pages 2549-2563, September.
    3. Long, Fei & Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Wang, Qing-Guo & Wu, Min, 2018. "Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 224-242.
    4. 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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