A New Approach to Multilinear Dynamical Systems and Control

• URL: http://arxiv.org/abs/2108.13583v1
• Date: Tue, 31 Aug 2021 02:08:28 GMT
• Title: A New Approach to Multilinear Dynamical Systems and Control
• Authors: Randy C. Hoover, Kyle Caudle, and Karen Braman
• Abstract summary: The 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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