Aperiodically intermittent stochastic stabilization via discrete time or delay feedback control

Abstract

In this paper, we present stochastic intermittent stabilization based on the feedback of the discrete time or the delay time. By using the stochastic comparison principle, the Itô formula, and the Borel- Cantelli lemma, we obtain two sufficient criteria for stochastic intermittent stabilization. The established criteria show that an unstable system can be stabilized by means of a stochastic intermittent noise via a discrete time feedback if the duration time τ is bounded by τ*. Similarly, stabilization via delay time feedback is equally possible if the lag time τ is bounded by τ**. The upper bound τ* and τ** can be computed numerically by solving corresponding equation.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61304070, 61773152), the Chinese Postdoctoral Science Foundation (Grant Nos. 2016M601698, 2017T100318), the Jiangsu Province Postdoctoral Science Foundation (Grant No. 1701078B), and the Project Funded by the Qing Lan Project of Jiangsu Province, China.

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Correspondence to Jinde Cao.

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Liu, L., Perc, M. & Cao, J. Aperiodically intermittent stochastic stabilization via discrete time or delay feedback control. Sci. China Inf. Sci. 62, 72201 (2019). https://doi.org/10.1007/s11432-018-9600-3

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Keywords

  • Brownian motion
  • stochastic stabilization
  • intermittent control
  • discrete time feedback
  • timedelay feedback