Positive Definiteness and Stability of Interval Tensors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911154156077056 |
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| author | Ye, Li Song, Yisheng |
| author_facet | Ye, Li Song, Yisheng |
| contents | In this paper, we focus on the positive definiteness and Hurwitz stability of interval tensors. First, we introduce auxiliary tensors $\mathcal{A}^z$ and establish equivalent conditions for the positive (semi-)definiteness of interval tensors. That is, an interval tensor is positive definite if and only if all $\mathcal{A}^z$ are positive (semi-)definite. For Hurwitz stability, it is revealed that the stability of the symmetric interval tensor $\mathcal{A}_s^I$ can deduce the stability of the interval tensor $\mathcal{A}^I$, and the stability of symmetric interval tensors is equivalent to that of auxiliary tensors $\tilde{\mathcal{A}}^z$. Finally, taking $4$th order $3$-dimensional interval tensors as examples, the specific sufficient conditions are built for their positive (semi-)definiteness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive Definiteness and Stability of Interval Tensors Ye, Li Song, Yisheng Optimization and Control In this paper, we focus on the positive definiteness and Hurwitz stability of interval tensors. First, we introduce auxiliary tensors $\mathcal{A}^z$ and establish equivalent conditions for the positive (semi-)definiteness of interval tensors. That is, an interval tensor is positive definite if and only if all $\mathcal{A}^z$ are positive (semi-)definite. For Hurwitz stability, it is revealed that the stability of the symmetric interval tensor $\mathcal{A}_s^I$ can deduce the stability of the interval tensor $\mathcal{A}^I$, and the stability of symmetric interval tensors is equivalent to that of auxiliary tensors $\tilde{\mathcal{A}}^z$. Finally, taking $4$th order $3$-dimensional interval tensors as examples, the specific sufficient conditions are built for their positive (semi-)definiteness. |
| title | Positive Definiteness and Stability of Interval Tensors |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.11540 |