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Stability Criteria for Systems with Multiple Probabilistic Intervals Time-varying Delay

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Abstract

The problem of stability for systems with multiple probabilistic intervals time-varying delay is investigated in this paper. First, it is assumed that the probability distributions of the time-varying delay falling into three intervals are known in prior. Two random variables obeying Bernoulli distributions, respectively, are introduced to characterize the probability of the time-varying delay taking values in three intervals. An equivalent new model including the existing ones as its special cases is given. Second, an appropriate Lyapunov-Krasovskii functional is constructed by exploiting more information of delay. Third, based on Lyapunov stability theory, several delay-distribution-dependent stability criteria are derived in the form of linear matrix inequalities by employing Reciprocally convex technique and Generalized Finsler's lemma. which can provide a larger upper bound of delay compared with the existed ones. Finally, a well-known numerical example is given to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Automation, Hangzhou Dianzi University, Hangzhou Zhejiang, 310018, China

    Zongming Yin, Xiefu Jiang & Fang Wang

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  1. Zongming Yin
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  2. Xiefu Jiang
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Correspondence to Xiefu Jiang.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor PooGyeon Park. This work was partially supported by the Key project of Natural Science Foundation of Zhejiang Province of China (Grant No. LZ13F030001) and the National Natural Science Foundation of the People's Republic of China (Grant No. 61673148).

Zongming Yin was born in Guizhou, China, in 1988. He received his B.S. degree from the School of Electronics and Information Engineering, North China Institute of Science and Technology in 2012, the M.S. degree from the School of Automation, Hangzhou Dianzi University in 2015. From 2015 to 2018, he was a lecturer with the School of mechanical engineering at Guizhou University of Engineering Science. He is currently pursuing a Ph.D. degree. His research interests include time-delay systems, sampled-data control systems, and T-S fuzzy systems.

Xiefu Jiang was born in Jiangsu, China, in 1963. He received his B.S. degree in Mathematics, Suzhou University, Jiangsu, in 1985, and his M.S. and Ph.D. degrees in Control Science and Engineering, Southeast University, Nanjing, China, in 1999 and 2002, respectively. From January 2002 to January 2004, he was a Postdoctoral Researcher Fellow at Tsinghua University, Beijing, China. From February 2004 to February 2007, he was a Postdoctoral Researcher Fellow at Central Queensland University, Rockhampton, QLD, Australia. Since March 2007, he has been a Professor in the School of Automation, Hangzhou Dianzi University, Hangzhou, China. His current research interests include time-delay systems, robust control, fuzzy control, sampled-data control systems, and networked control systems.

Fang Wang was born in Henan, China, in 1994. She received her B.S. degree from the School of Physical and Electronic Engineering, Xinyang Normal University in 2017. She is currently pursuing an M.S. degree. Her research interests include time-delay systems, and networked control systems.

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Yin, Z., Jiang, X. & Wang, F. Stability Criteria for Systems with Multiple Probabilistic Intervals Time-varying Delay. Int. J. Control Autom. Syst. 18, 877–885 (2020). https://doi.org/10.1007/s12555-019-0309-9

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  • DOI: https://doi.org/10.1007/s12555-019-0309-9

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