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Delay-dependent stability criteria of delayed positive systems with uncertain control inputs: Application in mosquito-borne morbidities control

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  • Dianavinnarasi, J.
  • Cao, Yang
  • Raja, R.
  • Rajchakit, G.
  • Lim, C.P.

Abstract

This note pays precise attention to derive the γ-exponential stability results of positive delayed systems via non-fragile control. By using Lyapunov–Krasovskii theory some necessary conditions are derived. Moreover, by using results from spectrum analysis the sufficient conditions for positive delayed systems with non-fragile control are analyzed. Our main intension is to locate the ideal application of this type of systems. In later part of this paper, the novel mathematical model which describes the life stages of Aedes Aegypti mosquitoes is proposed. In that model, the life shorting bacteria called Wolbachia is used as a biological control. By moderately thinking about the uncertain conditions in the biological control we implemented the non-fragile control. By applying the proposed results the γ-exponential stability of this population system is derived. Finally, some numerical examples are provided to expose the effectiveness of our predominant results.

Suggested Citation

  • Dianavinnarasi, J. & Cao, Yang & Raja, R. & Rajchakit, G. & Lim, C.P., 2020. "Delay-dependent stability criteria of delayed positive systems with uncertain control inputs: Application in mosquito-borne morbidities control," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s009630032030179x
    DOI: 10.1016/j.amc.2020.125210
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    References listed on IDEAS

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    1. Cao, Yang & Sriraman, R. & Samidurai, R., 2020. "Stability and stabilization analysis of nonlinear time-delay systems with randomly occurring controller gain fluctuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 36-51.
    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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    Cited by:

    1. Xie, Jiyang & Zhu, Shuqian & Zhang, Dawei, 2022. "A robust distributed secure interval observation approach for uncertain discrete-time positive systems under deception attacks," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Dianavinnarasi, J. & Raja, R. & Alzabut, J. & Cao, J. & Niezabitowski, M. & Bagdasar, O., 2022. "Application of Caputo–Fabrizio operator to suppress the Aedes Aegypti mosquitoes via Wolbachia: An LMI approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 462-485.

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