A subspace-based deterministic identification method is proposed for MIMO linear systems with time delay in their state variables. This method can estimate the matrices of the state-delayed system, its order and the amount of time delay. First, by extending the orthogonal decomposition subspace method for state-delayed systems, the augmented system matrices which include the original system matrices are identified. Then, an algorithm is presented to find a similarity transformation that converts the augmented matrices to a special form through which matrices of the state-delayed system can be extracted. The values of the time delay and model order are estimated by introducing appropriate criteria. Finally, three examples are provided to validate the proposed identification method.

中文翻译：

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MIMO线性状态延迟系统的基于子空间的确定性识别

针对状态变量存在时滞的MIMO线性系统，提出了一种基于子空间的确定性辨识方法。该方法可以估计状态延迟系统的矩阵、阶数和时间延迟量。首先，通过扩展状态延迟系统的正交分解子空间方法，识别出包含原始系统矩阵的增广系统矩阵。然后，提出了一种算法来寻找一种相似变换，该变换将增强矩阵转换为一种特殊形式，通过这种形式可以提取状态延迟系统的矩阵。通过引入适当的标准来估计时间延迟和模型阶次的值。最后，提供了三个例子来验证所提出的识别方法。