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On the controllability and observability of discrete-time linear time-delay systems

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  • Yuan-Ming Liu
  • I-Kong Fong

Abstract

This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.

Suggested Citation

  • Yuan-Ming Liu & I-Kong Fong, 2012. "On the controllability and observability of discrete-time linear time-delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 610-621.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:4:p:610-621
    DOI: 10.1080/00207721.2010.543490
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    Cited by:

    1. Long Sheng & Xiaoyu Ma, 2014. "Stability analysis and controller design of interval type-2 fuzzy systems with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(5), pages 977-993, May.

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