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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.17613 |
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| _version_ | 1866909327086845952 |
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| author | Nystrom, Anton Renganathan, Venkatraman Cantoni, Michael |
| author_facet | Nystrom, Anton Renganathan, Venkatraman Cantoni, Michael |
| contents | This paper investigates the stereographic projection of points along the Nyquist plots of single input single output (SISO) linear time invariant (LTI) systems subject to probabilistic uncertainty. At each frequency, there corresponds a complex-valued random variable with given probability distribution in the complex plane. The chordal distance between the stereographic projections of this complex value and the corresponding value for a nominal model, as per the well-known Nu-Gap metric of Vinnicombe, is also a random quantity. The main result provides the cumulative density function (CDF) of the chordal distance at a given frequency. Such a stochastic distance framework opens up a fresh and a fertile research direction on probabilistic robust control theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stereographic Projection of Probabilistic Frequency-Domain Uncertainty Nystrom, Anton Renganathan, Venkatraman Cantoni, Michael Systems and Control This paper investigates the stereographic projection of points along the Nyquist plots of single input single output (SISO) linear time invariant (LTI) systems subject to probabilistic uncertainty. At each frequency, there corresponds a complex-valued random variable with given probability distribution in the complex plane. The chordal distance between the stereographic projections of this complex value and the corresponding value for a nominal model, as per the well-known Nu-Gap metric of Vinnicombe, is also a random quantity. The main result provides the cumulative density function (CDF) of the chordal distance at a given frequency. Such a stochastic distance framework opens up a fresh and a fertile research direction on probabilistic robust control theory. |
| title | Stereographic Projection of Probabilistic Frequency-Domain Uncertainty |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.17613 |