Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control

Yuyuan Li; Jianqiu Lu; Chunhai Kou; Xuerong Mao; Jiafeng Pan

doi:10.1002/oca.2293

Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control

Yuyuan Li, Jianqiu Lu, Chunhai Kou, Xuerong Mao, Jiafeng Pan

Mathematics And Statistics

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Abstract

This paper aims to stabilize hybrid stochastic differential equations (SDEs) with norm bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of an SDE and the controlled system will be robustly exponentially stable in mean-square. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results.

Original language	English
Pages (from-to)	847-859
Number of pages	13
Journal	Optimal Control Applications and Methods
Volume	38
Issue number	5
Early online date	21 Nov 2016
DOIs	https://doi.org/10.1002/oca.2293
Publication status	Published - 1 Oct 2017

Keywords

stochastic systems
Markovian jumping systems
uncertain systems
robust stabilization
discrete-time feedback control

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10.1002/oca.2293

Li-etal-OCAM-2016-Robust-stabilization-of-hybrid-uncertain-stochastic-systemsAccepted author manuscript, 806 KB

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title = "Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control",

abstract = "This paper aims to stabilize hybrid stochastic differential equations (SDEs) with norm bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of an SDE and the controlled system will be robustly exponentially stable in mean-square. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results.",

keywords = "stochastic systems, Markovian jumping systems, uncertain systems, robust stabilization, discrete-time feedback control",

author = "Yuyuan Li and Jianqiu Lu and Chunhai Kou and Xuerong Mao and Jiafeng Pan",

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AU - Li, Yuyuan

AU - Lu, Jianqiu

AU - Kou, Chunhai

AU - Mao, Xuerong

AU - Pan, Jiafeng

N1 - Copyright © 2016 John Wiley & Sons, Ltd. Li, Y., Lu, J., Kou, C., Mao, X., and Pan, J. (2017) Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control. Optim. Control Appl. Meth., 38: 847–859. doi: 10.1002/oca.2293

PY - 2017/10/1

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N2 - This paper aims to stabilize hybrid stochastic differential equations (SDEs) with norm bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of an SDE and the controlled system will be robustly exponentially stable in mean-square. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results.

AB - This paper aims to stabilize hybrid stochastic differential equations (SDEs) with norm bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of an SDE and the controlled system will be robustly exponentially stable in mean-square. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results.

KW - stochastic systems

KW - Markovian jumping systems

KW - uncertain systems

KW - robust stabilization

KW - discrete-time feedback control

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DO - 10.1002/oca.2293

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VL - 38

SP - 847

EP - 859

JO - Optimal Control Applications and Methods

JF - Optimal Control Applications and Methods

IS - 5

ER -

Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control

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Numerical Analysis of Stochastic Differential Equations: New Challenges

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Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control

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Numerical Analysis of Stochastic Differential Equations: New Challenges

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