• myGriffith
    • Staff portal
    • Contact Us⌄
      • Future student enquiries 1800 677 728
      • Current student enquiries 1800 154 055
      • International enquiries +61 7 3735 6425
      • General enquiries 07 3735 7111
      • Online enquiries
      • Staff phonebook
    View Item 
    •   Home
    • Griffith Research Online
    • Journal articles
    • View Item
    • Home
    • Griffith Research Online
    • Journal articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

  • All of Griffith Research Online
    • Communities & Collections
    • Authors
    • By Issue Date
    • Titles
  • This Collection
    • Authors
    • By Issue Date
    • Titles
  • Statistics

  • Most Popular Items
  • Statistics by Country
  • Most Popular Authors
  • Support

  • Contact us
  • FAQs
  • Admin login

  • Login
  • Investigating the effects of time-delays on stochastic stability and designing l1-gain controllers for positive discrete-time Markov jump linear systems with time-delay

    Author(s)
    Zhu, Shuqian
    Han, Qing-Long
    Zhang, Chenghui
    Griffith University Author(s)
    Han, Qing-Long
    Year published
    2016
    Metadata
    Show full item record
    Abstract
    This paper is concerned with stochastic stability, l1-gain performance analysis and positivity-preserving l1-gain controller design for a positive discrete-time Markov jump linear system with time-delay. First, necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co-positive stochastic Lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time-delay and the transition probability. It is revealed that stochastic stability of the positive ...
    View more >
    This paper is concerned with stochastic stability, l1-gain performance analysis and positivity-preserving l1-gain controller design for a positive discrete-time Markov jump linear system with time-delay. First, necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co-positive stochastic Lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time-delay and the transition probability. It is revealed that stochastic stability of the positive discrete-time Markov jump linear system with time-delay is influenced by the size of time-delay and it is demonstrated by an example that the effect of time-delay on stochastic stability can be either positive or negative. Second, exact computation on an l1-gain index of a stochastically stable positive discrete-time Markov jump linear system with time-delay is presented, and a necessary and sufficient condition for the l1-gain performance is derived in the form of linear programming. Third, an iterative algorithm is proposed to design a positivity-preserving l1-gain controller, and in single-input case, an optimal controller is obtained analytically such that the closed-loop system achieves the minimal l1-gain performance. Then, a modified pest’s structured population dynamic model is developed to illustrate the effectiveness of the designed method.
    View less >
    Journal Title
    Information Sciences
    Volume
    355-356
    DOI
    https://doi.org/10.1016/j.ins.2016.03.044
    Subject
    Numerical and Computational Mathematics not elsewhere classified
    Mathematical Sciences
    Information and Computing Sciences
    Engineering
    Publication URI
    http://hdl.handle.net/10072/172068
    Collection
    • Journal articles

    Footer

    Disclaimer

    • Privacy policy
    • Copyright matters
    • CRICOS Provider - 00233E
    • TEQSA: PRV12076

    Tagline

    • Gold Coast
    • Logan
    • Brisbane - Queensland, Australia
    First Peoples of Australia
    • Aboriginal
    • Torres Strait Islander