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The express decay effect of time delays for globally exponentially stable nonlinear stochastic systems

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Abstract

This paper considers the express decay effect of time-varying delays for nonlinear stochastic systems. Given a globally exponentially stable nonlinear stochastic system, we investigate upper bounds of the time delays that the perturbed stochastic system can withstand to sustain its previous stability or decay rate faster than before. The upper bounds of the time delays are obtained directly from the global exponential stability coefficients conditions and expressed by transcendental equations containing adjustable parameters. Finally, a numerical simulation is conducted to illustrate the effectiveness of the theoretical results.

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Acknowledgment

This work was supported by the National Natural Science Foundation of China under Grant 61873271 and the Fundamental Research Funds for the Central Universities 2018XK QYMS15.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Kaili Sun & Song Zhu

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  1. Kaili Sun
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  2. Song Zhu
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Correspondence to Song Zhu.

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This article is part of the Topical Collection: Special Issue on Networked Cyber-Physical Systems

Guest Editors: Heng Zhang, Mohammed Chadli, Zhiguo Shi, Yanzheng Zhu, and Zhaojian Li

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Sun, K., Zhu, S. The express decay effect of time delays for globally exponentially stable nonlinear stochastic systems. Peer-to-Peer Netw. Appl. 12, 1716–1725 (2019). https://doi.org/10.1007/s12083-019-00735-1

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  • DOI: https://doi.org/10.1007/s12083-019-00735-1

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