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Subspace-based identification of discrete time-delay system

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Abstract

We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Qiang Liu & Jia-chen Ma

  2. School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai, 264209, China

    Jia-chen Ma

Authors
  1. Qiang Liu
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  2. Jia-chen Ma
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Correspondence to Qiang Liu.

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ORCID: Qiang LIU, http://orcid.org/0000-0003-2464-8007

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Liu, Q., Ma, Jc. Subspace-based identification of discrete time-delay system. Frontiers Inf Technol Electronic Eng 17, 566–575 (2016). https://doi.org/10.1631/FITEE.1500358

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  • DOI: https://doi.org/10.1631/FITEE.1500358

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