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Exponential stability of uncertain differential equation

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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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Acknowledgments

This work was supported by National Natural Science Foundation of China Grant Nos. 61273044, 61262023 and 61462086.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Yuhong Sheng

  2. College of Mathematical and System Sciences, Xinjiang University, Ürümqi, 830046, China

    Yuhong Sheng

  3. School of Information, Renmin University of China, Beijing, 100872, China

    Jinwu Gao

Authors
  1. Yuhong Sheng
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  2. Jinwu Gao
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Correspondence to Yuhong Sheng.

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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

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