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Almost sure stability for uncertain differential equation

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Abstract

Uncertain differential equation is a type of differential equation driven by Liu process. So far, concepts of stability and stability in mean for uncertain differential equations have been proposed. This paper aims at providing a concept of almost sure stability for uncertain differential equation. A sufficient condition is given for an uncertain differential equation being almost surely stable, and some examples are given to illustrate the effectiveness of the sufficient condition.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China Grants No.71171003, No.61203139, No.71371141, and No.71001080, and the Natural Science Foundation of Anhui Universities Grant No.KJ2013B023.

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Correspondence to Hongjian Liu.

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Liu, H., Ke, H. & Fei, W. Almost sure stability for uncertain differential equation. Fuzzy Optim Decis Making 13, 463–473 (2014). https://doi.org/10.1007/s10700-014-9188-y

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  • DOI: https://doi.org/10.1007/s10700-014-9188-y

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