### Abstract

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p > 1 and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent.

Original language | English |
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Pages (from-to) | 909-919 |

Number of pages | 11 |

Journal | IET Control Theory and Applications |

Volume | 14 |

Issue number | 6 |

Early online date | 6 Jan 2020 |

DOIs | |

Publication status | Published - 16 Apr 2020 |

### Keywords

- stochastic differential equations
- exponential stabilisation
- Markovian switching
- periodic stochastic systems
- feedback control
- discrete-time observations

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## Cite this

*IET Control Theory and Applications*,

*14*(6), 909-919. https://doi.org/10.1049/iet-cta.2019.0803