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l₁-gain controller design for 2-D Markov jump positive systems with directional delays

  • Zhaoxia Duan
    ,
  • Choon Ki Ahn
    ,
  • Zhengrong Xiang
    ,
  • Imran Ghous
Research Output: Contribution to journal Article Peer-review

Abstract

This article is concerned with the stochastic stability and l1 -gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact l1 -gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the l1 -gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal l1 -gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples.

Publication Information

Output type

Research Output: Contribution to journal Article Peer-review

Original language

English

Pages from-to (Number of pages)

Pages 7600-7613 (14 pages)

Journal (Volume, Issue Number)

IEEE Transactions on Systems, Man, and Cybernetics: Systems (Volume 52, Issue 12)

Publication milestones

  • Published - 30/03/2022

Publication status

Published - 30/03/2022

ISSN

2168-2216

External Publication IDs

  • ORCID: /0000-0002-8215-4315/work/118801513
  • Scopus: 85127476924

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