Real Eventual Exponential Positivity of Complex-valued Laplacians: Applications to Consensus in Multi-agent Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912075490525184 |
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| author | Saxena, Aditi Tripathy, Twinkle Anguluri, Rajasekhar |
| author_facet | Saxena, Aditi Tripathy, Twinkle Anguluri, Rajasekhar |
| contents | In this paper, we explore the property of eventual exponential positivity (EEP) in complex matrices. We show that this property holds for the real part of the matrix exponential for a certain class of complex matrices. Next, we present the relation between the spectral properties of the Laplacian matrix of an unsigned digraph with complex edge-weights and the property of real EEP. Finally, we show that the Laplacian flow system of a network is stable when the negated Laplacian admits real EEP. Numerical examples are presented to demonstrate the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real Eventual Exponential Positivity of Complex-valued Laplacians: Applications to Consensus in Multi-agent Systems Saxena, Aditi Tripathy, Twinkle Anguluri, Rajasekhar Systems and Control In this paper, we explore the property of eventual exponential positivity (EEP) in complex matrices. We show that this property holds for the real part of the matrix exponential for a certain class of complex matrices. Next, we present the relation between the spectral properties of the Laplacian matrix of an unsigned digraph with complex edge-weights and the property of real EEP. Finally, we show that the Laplacian flow system of a network is stable when the negated Laplacian admits real EEP. Numerical examples are presented to demonstrate the results. |
| title | Real Eventual Exponential Positivity of Complex-valued Laplacians: Applications to Consensus in Multi-agent Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.13700 |