On the Stability of Multilinear Dynamical Systems

Can Chen

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arXiv · 2105.01041

On the Stability of Multilinear Dynamical Systems

Can Chen

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Abstract

This paper investigates the stability properties of discrete-time multilinear dynamical systems via tensor spectral theory. In particular, if the dynamic tensor of a multilinear dynamical system is orthogonally decomposable (odeco), we can construct its explicit solution by exploiting tensor Z-eigenvalues and Z-eigenvectors. Based on the form of the explicit solution, we illustrate that the Z-eigenvalues of the dynamic tensor play a significant role in the stability analysis, offering necessary and sufficient conditions. In addition, by utilizing the upper bounds of Z-spectral radii, we are able to determine the asymptotic stability of the multilinear dynamical system efficiently. Furthermore, we extend the stability results to the multilinear dynamical systems with non-odeco dynamic tensors by exploiting tensor singular values. We demonstrate our results via numerical examples.

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BibTeX RIS

Can Chen. 2021-05-03. On the Stability of Multilinear Dynamical Systems. https://arxiv.org/abs/2105.01041

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