### Abstract

*the feedback controls based on the discrete-time observations of the state*. However, the feedback controls still

*depend on the continuous-time observations of the mode*. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the

*discrete-time observations of*

both state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE.

both state and mode

Language | English |
---|---|

Number of pages | 15 |

Journal | Control Theory and Applications |

Early online date | 1 Nov 2016 |

DOIs | |

Publication status | E-pub ahead of print - 1 Nov 2016 |

### Fingerprint

### Keywords

- stabilisation
- feedback control
- discrete-time observations
- hybrid stochastic differential equations
- Brownian motion

### Cite this

}

**Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode.** / Song, Gongfei; Zheng, Bo-Chao; Luo, Qi; Mao, Xuerong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode

AU - Song, Gongfei

AU - Zheng, Bo-Chao

AU - Luo, Qi

AU - Mao, Xuerong

N1 - This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory and Applications and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Mao [10] recently initiated the study of the mean-square exponential stabilisation of continuous-time hybrid stochastic differential equations (SDEs) by the feedback controls based on the discrete-time observations of the state. However, the feedback controls still depend on the continuous-time observations of the mode. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the discrete-time observations ofboth state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE.

AB - Mao [10] recently initiated the study of the mean-square exponential stabilisation of continuous-time hybrid stochastic differential equations (SDEs) by the feedback controls based on the discrete-time observations of the state. However, the feedback controls still depend on the continuous-time observations of the mode. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the discrete-time observations ofboth state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE.

KW - stabilisation

KW - feedback control

KW - discrete-time observations

KW - hybrid stochastic differential equations

KW - Brownian motion

UR - http://digital-library.theiet.org/content/journals/iet-cta

U2 - 10.1049/iet-cta.2016.0635

DO - 10.1049/iet-cta.2016.0635

M3 - Article

JO - IET Control Theory and Applications

T2 - IET Control Theory and Applications

JF - IET Control Theory and Applications

SN - 1751-8644

ER -