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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/2402.04074 |
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| _version_ | 1866914782509006848 |
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| author | Li, Junhui Lu, Jieying Su, Weizhou |
| author_facet | Li, Junhui Lu, Jieying Su, Weizhou |
| contents | In this paper, the feedback stabilization of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) system cascaded by a linear stochastic system is studied in the mean-square sense. Here, the linear stochastic system can model a class of correlated stochastic uncertainties such as channel uncertainties induced by packet loss and random transmission delays in networked systems. By proposing a key parameter called coefficient of frequency variation to characterize the correlation of the stochastic uncertainties, we present a necessary and sufficient condition of the mean-square stability for this MIMO stochastic feedback system. After then a necessary and sufficient condition for the mean-square stabilizability is provided, which reveals a fundamental limit imposed by the system's unstable poles, nonminimum-phase (NMP) zeros, relative degrees (input delays), and the coefficient of frequency variation of the stochastic uncertainties. A numerical example is presented to illustrate the fundamental constraints in the mean-square stabilizability of MIMO networked systems with parallel communication channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-Square Stability and Stabilizability for LTI and Stochastic Systems Connected in Feedback Li, Junhui Lu, Jieying Su, Weizhou Systems and Control In this paper, the feedback stabilization of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) system cascaded by a linear stochastic system is studied in the mean-square sense. Here, the linear stochastic system can model a class of correlated stochastic uncertainties such as channel uncertainties induced by packet loss and random transmission delays in networked systems. By proposing a key parameter called coefficient of frequency variation to characterize the correlation of the stochastic uncertainties, we present a necessary and sufficient condition of the mean-square stability for this MIMO stochastic feedback system. After then a necessary and sufficient condition for the mean-square stabilizability is provided, which reveals a fundamental limit imposed by the system's unstable poles, nonminimum-phase (NMP) zeros, relative degrees (input delays), and the coefficient of frequency variation of the stochastic uncertainties. A numerical example is presented to illustrate the fundamental constraints in the mean-square stabilizability of MIMO networked systems with parallel communication channels. |
| title | Mean-Square Stability and Stabilizability for LTI and Stochastic Systems Connected in Feedback |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2402.04074 |