Counting Zeros Using Observability and Block Toeplitz Matrices

• 成果类型: Article
• 署名作者: Sanjeevini, Sneha; Bernstein, Dennis S.
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2989269
• 发表日期: 2021
• 页码: 1301-1305
• 关键词: Filtering theory; Poles and zeros; observability; Linear systems; DELAYS; Markov processes; Block Toeplitz matrix; infinite zeros; Smith– McMillan form; transmission zeros

摘要

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.