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Exponential stability analysis for positive systems with delays

Exponential stability analysis for positive systems with delays

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  • Author(s): S. Zhu 1 ; Z. Li 2 ; C. Zhang 3
    • View affiliations
    • Affiliations: 1: School of Mathematics, Shandong University, Jinan, People's Republic of China
      2: School of Statistics, Shandong University of Finance and Economics, Jinan, People's Republic of China
      3: School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China
  • Source: Volume 6, Issue 6, 12 April 2012, p. 761 – 767
    DOI:  10.1049/iet-cta.2011.0133 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

This study investigates the exponential stability analysis problem for continuous-time and discrete-time positive linear systems with delays. For given decay rate, necessary conditions for exponential stability of such systems are presented based on the asymptotical stability results of positive linear time-delay systems, and sufficient conditions are provided by using Lyapunov–Krasovskii functional method. It is shown that, the exponential stability with given decay rate of positive linear time-delay systems has to do with the delays. Some illustrative examples are given to show the correctness of the obtained theoretical results.

Inspec keywords: asymptotic stability; delay systems; continuous time systems; discrete time systems; delays; Lyapunov methods; linear systems

Other keywords: decay rate; exponential stability analysis problem; delays; asymptotical stability; Lyapunov-Krasovskii functional method; continuous-time positive linear time-delay systems; discrete-time positive linear time-delay systems

Subjects: Discrete control systems; Distributed parameter control systems; Stability in control theory

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