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arXiv · 2108.13583

A New Approach to Multilinear Dynamical Systems and Control

Randy C. Hoover·Kyle Caudle·Karen Braman
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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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Randy C. Hoover, Kyle Caudle, Karen Braman. 2021-08-31. A New Approach to Multilinear Dynamical Systems and Control. https://arxiv.org/abs/2108.13583

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