Nyquist stability criteria for control systems with stochastic delays

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Abstract

We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages270-275
Number of pages6
ISBN (Electronic)978-1-5386-1395-5
ISBN (Print)978-1-5386-1396-2
DOIs
Publication statusPublished - 18 Jan 2019
Event57th IEEE Conference on Decision and Control, (CDC2018) - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, (CDC2018)
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

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  • Cite this

    Antunes, D. J. (2019). Nyquist stability criteria for control systems with stochastic delays. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 270-275). [8619247] Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2018.8619247