Abstract
Uncertain differential equation with jumps, as a crucial tool to deal with a discontinuous uncertain system, is a type of differential equation driven by both canonical Liu process and uncertain renewal process. So far, a concept of stability in measure for an uncertain differential equation with jumps has been proposed. As a supplement, this paper proposes a concept of almost sure stability for an uncertain differential equation with jumps. A sufficient condition is derived for an uncertain differential equation with jumps being stable almost surely. As a corollary, a sufficient condition is also given for a linear uncertain differential equation with jumps being stable almost surely.
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Acknowledgments
This work was supported by National Natural Science Foundation of China (Grant No. 71171191, Grant No. 71371141, and Grant No. 71001080).
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Communicated by V. Loia.
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Ji, X., Ke, H. Almost sure stability for uncertain differential equation with jumps. Soft Comput 20, 547–553 (2016). https://doi.org/10.1007/s00500-014-1521-4
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DOI: https://doi.org/10.1007/s00500-014-1521-4