Affiliation:
1. School of Mathematics and Computational Science, Hunan University of Science and Technology , Xiangtan, Hunan 411201, China
Abstract
Abstract
The Smith form of an $n$-$D$ polynomial matrix plays an important role in many areas of mathematics and engineering. In this paper, we investigate the recursive equivalence problem of $n$-dimensional polynomial matrices, i.e. if diag$(1,B)$ is equivalent to diag$(1,1,C)$, is B equivalent to diag$(1,C)$? We give a negative answer to this question by explicitly constructing a four-dimensional polynomial matrix which is not equivalent to its Smith form.
Funder
National Natural Science Foundation of China
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Control and Optimization,Control and Systems Engineering