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Design of an optimal preview controller for linear discrete-time descriptor systems with state delay

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  • Mengjuan Cao
  • Fucheng Liao

Abstract

In this paper, the linear discrete-time descriptor system with state delay is studied, and a design method for an optimal preview controller is proposed. First, by using the discrete lifting technique, the original system is transformed into a general descriptor system without state delay in form. Then, taking advantage of the first-order forward difference operator, we construct a descriptor augmented error system, including the state vectors of the lifted system, error vectors, and desired target signals. Rigorous mathematical proofs are given for the regularity, stabilisability, causal controllability, and causal observability of the descriptor augmented error system. Based on these, the optimal preview controller with preview feedforward compensation for the original system is obtained by using the standard optimal regulator theory of the descriptor system. The effectiveness of the proposed method is shown by numerical simulation.

Suggested Citation

  • Mengjuan Cao & Fucheng Liao, 2015. "Design of an optimal preview controller for linear discrete-time descriptor systems with state delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(5), pages 932-943, April.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:5:p:932-943
    DOI: 10.1080/00207721.2013.801097
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    Cited by:

    1. Guo Yujian & Liao Fucheng, 2018. "Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems," Journal of Systems Science and Information, De Gruyter, vol. 6(2), pages 178-192, April.
    2. Yuedou Pan & Mengtong Pei & Li Li & Yanrong Lu, 2020. "Preview Tracking Control for Discrete-Time Multirate Systems: An Internal Model-Based Approach," Mathematics, MDPI, vol. 8(9), pages 1-20, August.
    3. Jiang Wu & Hao Xie & Jinming Liang & Zhiqiang Li, 2024. "Preview Control for Cyber–Physical Systems under Periodic Denial-of-Service Attacks," Mathematics, MDPI, vol. 12(17), pages 1-20, August.
    4. Xu Haishan & Liao Fucheng, 2019. "Optimal Tracking Control for Discrete-time Systems with Time-delay Based on the Preview Control Method," Journal of Systems Science and Information, De Gruyter, vol. 7(5), pages 452-461, October.

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