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 language | English |
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| Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |
| Place of Publication | Piscataway |
| Publisher | Institute of Electrical and Electronics Engineers |
| Pages | 270-275 |
| Number of pages | 6 |
| ISBN (Electronic) | 978-1-5386-1395-5 |
| ISBN (Print) | 978-1-5386-1396-2 |
| DOIs | |
| Publication status | Published - 18 Jan 2019 |
| Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57 |
Conference
| Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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| Abbreviated title | CDC 2018 |
| Country/Territory | United States |
| City | Miami |
| Period | 17/12/18 → 19/12/18 |
Funding
Duarte J. Antunes is Assistant Professor at the Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, the Netherlands. {D. Antunes}@tue.nl. This work was funded by the European Unions Horizon 2020 Framework Programme for Research and Innovation under grant agreement No 674875.