Abstract
Uncertain differential equation is a type of differential equations involving uncertain processes. So far, the concepts of stability in measure and stability in mean have been proposed for uncertain differential equations. This paper proposes a new type of stability for uncertain differential equation, named exponential stability. Some examples are given to illustrate the concept, and the relationships between exponential stability, stability in measure and stability in mean are discussed. Besides, a sufficient and necessary condition for a linear uncertain differential equation being exponentially stable is derived.
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This work was supported by National Natural Science Foundation of China Grant Nos. 61273044, 61262023 and 61462086.
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Communicated by V. Loia.
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Sheng, Y., Gao, J. Exponential stability of uncertain differential equation. Soft Comput 20, 3673–3678 (2016). https://doi.org/10.1007/s00500-015-1727-0
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DOI: https://doi.org/10.1007/s00500-015-1727-0