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Counting Zeros Using Observability and Block Toeplitz Matrices
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DOI：10.1109/TAC.2020.2989269.png)
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Abstract
En 中文
Transmission zeros can be counted by using the Smith-McMillan form, pole/zero modules, or the dimension of the largest output-nulling invariant subspace. This article provides an alternative approach by showing that the number of transmission zeros of a multiple-input-multiple-output (MIMO) transfer function is given in terms of the defect of a block Toeplitz matrix and the defect of an augmented matrix consisting of an observability matrix and the block Toeplitz matrix. It is also shown that the number of infinite zeros is related to the defect of a block Toeplitz matrix. These results are illustrated with a numerical example.
Keywords:
Filtering theory
Poles and zeros
Observability
Linear systems
Delays
Markov processes
Block Toeplitz matrix
infinite zeros
Smith– McMillan form
transmission zeros
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