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Difference flatness of discrete-time linear time-delay systems and transformation to fully actuated systems

Author

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  • Yu Liu
  • Zhao-Yan Li
  • Xijing Hu

Abstract

This paper investigates the difference flatness of discrete-time linear time-delay systems (TDSs). Initially, by employing matrix augmentation techniques and model reduction methods, the discrete-time linear TDSs can be transformed into the discrete-time linear delay-free systems while preserving controllability equivalence. Subsequently, a coprime factorisation approach for the transfer function matrix of discrete-time linear delay-free systems is utilised to construct the flat output of the discrete-time linear TDSs. Based on this, the discrete-time linear TDSs can be equivalently transformed into the discrete-time fully actuated system (FAS) with the constructed flat output as the generalised state, and the pole assignment problem of discrete-time TDSs can be directly addressed. Numerical examples demonstrates the effectiveness of the proposed approach.

Suggested Citation

  • Yu Liu & Zhao-Yan Li & Xijing Hu, 2025. "Difference flatness of discrete-time linear time-delay systems and transformation to fully actuated systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(13), pages 3243-3256, October.
    • Handle: RePEc:taf:tsysxx:v:56:y:2025:i:13:p:3243-3256
    DOI: 10.1080/00207721.2025.2530187
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