Kronecker products of defective matrices: Some spectral properties and their implications on observability

Abstract:

The eigenvector analysis of the Kronecker product of defective matrices is revisited, and is brought to bear in characterizing observability of linear systems with Kronecker-product state matrices. Specifically, a new proof is given for a classical result on the eigenspace dimension for the Kronecker product of two Jordan chains, which highlights that the dimension is essentially dependent on the off-diagonal entries' zero pattern. Based on the spectral characterization of the Kronecker product, observability conditions are then developed for linear systems with Kronecker-product state matrices. Simple examples from two application domains are also included, to illustrate how the spectral and observability results can inform stochastic-systems analysis. © 2012 AACC American Automatic Control Council).

Año de publicación:

2012

Keywords:

Fuente:

scopus