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Stabilization of stochastically singular nonlinear jump systems with unknown parameters and continuously distributed delays

  • Control Theory
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Abstract

In this paper, the problem of robustly asymptotic stabilization for a class of stochastically nonlinear singular jump systems is investigated. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. Based on the Lyapunov-Krasovskii functional and stochastic analysis theory as well as a state feedback control technique, some new sufficient conditions are derived to ensure the asymptotic stability of the trivial solution in the mean square. A key feature of this paper is that singular, nonlinear, noise perturbations, unknown parameters and continuously distributed delays are all considered. In particular, the obtained stabilization criteria in this paper are expressed in terms of LMIs, which can be solved easily by recently developed algorithms. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results. Moreover, the second example shows that delay-dependent stabilization criteria are less conservative than delay-independent criteria.

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Authors and Affiliations

  1. School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Quanxin Zhu

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  1. Quanxin Zhu
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Correspondence to Quanxin Zhu.

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Recommended by Editorial Board member Duk-Sun Shim under the direction of Editor Yoshito Ohta.

This work was jointly supported by the National Natural Science Foundation of China, the National Natural Science Foundation of Zhejiang Province (LY12F03010), the Natural Science Foundation of Ningbo (2012A610032).

Quanxin Zhu received his Ph.D. degree from Sun Yat-Sen University, Guangzhou, China, in 2005. He is currently a Professor with Nanjing Normal University. He is the author or co-author of more than 50 research papers, a member of IEEE and a reviewer of Mathematical Reviews, Zentralblatt Math. His current research interests include random processes, stochastic controls, stochastic differential equations, stochastic partial differential equations, Markovian jump systems, and stochastic neural networks. Prof. Zhu is an Associate Editor of Transnational Journal of Mathematical Analysis and Applications, and a reviewer of more than 30 other journals.

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Zhu, Q. Stabilization of stochastically singular nonlinear jump systems with unknown parameters and continuously distributed delays. Int. J. Control Autom. Syst. 11, 683–691 (2013). https://doi.org/10.1007/s12555-012-9114-4

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  • DOI: https://doi.org/10.1007/s12555-012-9114-4

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