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CLC number: TP242.6

On-line Access: 2016-06-06

Received: 2015-10-23

Revision Accepted: 2016-03-14

Crosschecked: 2016-05-06

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Qiang Liu


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Frontiers of Information Technology & Electronic Engineering  2016 Vol.17 No.6 P.566-575


Subspace-based identification of discrete time-delay system

Author(s):  Qiang Liu, Jia-chen Ma

Affiliation(s):  School of Astronautics, Harbin Institute of Technology, Harbin 150001, China; more

Corresponding email(s):   lqianghit@163.com

Key Words:  Identification problems, Time-delay systems, Subspace identification method, Alternate convex search, Least squares

Qiang Liu, Jia-chen Ma. Subspace-based identification of discrete time-delay system[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(6): 566-575.

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T1 - Subspace-based identification of discrete time-delay system
A1 - Qiang Liu
A1 - Jia-chen Ma
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1500358

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.

This paper is concerned with the identification problems for a class of linear stochastic time-delay systems with unknown delayed states. The time-delay system is expressed as a delay differential equation with a single delay in state vector and conventional subspace identification method is utilized to estimate the augmented system matrices. The time-delay system matrices, under the same state space basis, are recovered from the Kalman state sequences and input-output data. Finally, authors validated their theoretical results by providing numerical examples.




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