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New Stochastic Stability Criteria for Nonlinear Neutral Markovian Jump Systems

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Abstract

This paper address the stochastic stability of neutral markovian jumping systems with nonlinear perturbations. By constructing novel Lyapunov functionals which contain an augmented Lyapunov functional, and combining with the new inequalities, new delay-dependent stochastic stability criteria for the nominal systems are obtained. The asymptotically stable condition is a special case for the stochastic stability condition as the systems without markovian jump. Numerical examples show that the derived conditions are much less conservative than those given in the existing literature.

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Authors and Affiliations

  1. School of Mathematics and Computation Science, Anqing Normal University, Anqing, 246133, China

    Hongmei Zhang

  2. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, 650500, China

    Lianglin Xiong

Authors
  1. Hongmei Zhang
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  2. Jinde Cao
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  3. Lianglin Xiong
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Corresponding author

Correspondence to Lianglin Xiong.

Additional information

Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. This work is jointly supported by National Nature Science Foundation under Grant No. 11461082, 11601474 and 61570396, supported by the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002, Key laboratory of numerical simulation of Sichuan Province under Grant No. 2017KF002.

Hongmei Zhang received the bachelor degree in information and computing science from Northwestern University, Shaanxi, China, in 2003 and her Master degree in Applied Mathematics from East Normal University, Shanghai, China in 2010. She is a staff of School of mathematics and computing science, Anqing Normal University in July 2003-present. Her research interest is stability theory and its application to the delay system, the nonlinear control and complex networks and so on.

Jinde Cao received the B.S. degree from Anhui Normal University, Wuhu, China, the M.S. degree from Yunnan University, Kunming, China, and the Ph.D. degree from Sichuan University, Chengdu, China, all in mathematics/applied mathematics, in 1986, 1989, and 1998, respectively. He is an Endowed Chair Professor, the Dean of School of Mathematics and the Director of the Research Center for Complex Systems and Network Sciences at Southeast University. From March 1989 to May 2000, he was with the Yunnan University. In May 2000, he joined the School of Mathematics, Southeast University, Nanjing, China. From July 2001 to June 2002, he was a Postdoctoral Research Fellow at Chinese University of Hong Kong, Hong Kong. Professor Cao was an Associate Editor of the IEEE Transactions on Neural Networks, and Neurocomputing. He is an Associate Editor of the IEEE Transactions on Cybernetics, IEEE Transactions on Cognitive and Developmental Systems, Journal of the Franklin Institute, Mathematics and Computers in Simulation, Cognitive Neurodynamics, and Neural Networks. He is a Fellow of IEEE, a Member of the Academy of Europe, a Member of European Academy of Sciences and Arts and a Fellow of Pakistan Academy of Sciences. He has been named as Highly-Cited Researcher in Engineering,Computer Science, and Mathematics by Thomson Reuters/Clarivate Analytics. He received the National Innovation Award of China (2017).

Lianglin Xiong received the bachelor degree in Mathematics and Applied Mathematics from Neijiang Normal University, Sichuan, China, in 2004 and his Master and Doctoral degree in Applied Mathematics from University of Electronic Science and Technology of China, Sichuan, China, in 2007 and 2009, respectively. He is a staff of School of Mathematics and Computer Science, Yunnan Minzu University in March 2010-present. In 2012, he was appointed as a professor and master tutor of Applied Mathematics. His research interest is Stability theorem and its application to the delay system, the robustness control, hybrid systems and complex networks and so on.

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Zhang, H., Cao, J. & Xiong, L. New Stochastic Stability Criteria for Nonlinear Neutral Markovian Jump Systems. Int. J. Control Autom. Syst. 17, 630–638 (2019). https://doi.org/10.1007/s12555-018-0442-x

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  • DOI: https://doi.org/10.1007/s12555-018-0442-x

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