Year: 2021
Type: preprint
Abstract: The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown that under the right tensor multiplication operator, a third order tensor can be written as a product of third order tensors that is analogous to a traditional matrix eigenvalue decomposition where the "eigenvectors" become eigenmatrices and the "eigenvalues" become eigen-tuples. This new development allows for a proper tensor eigenvalue decomposition to be defined and has natural extension to linear systems theory through a \textit{tensor-exponential}. Through this framework we extend many of traditional techniques used in linear system theory to their multilinear counterpart.
Source: arXiv (Cornell University)
Authors: Hoover, Randy C., Caudle, Kyle, Braman, Karen
Institution: South Dakota School of Mines and Technology
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3196863862