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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.

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.

基于子空间的离散时滞系统辨识

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