Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

Quanxin Zhu (), Fubao Xi and Xiaodi Li
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Quanxin Zhu: Ningbo University
Fubao Xi: Beijing Institute of Technology
Xiaodi Li: Shandong Normal University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 10, 154-174

Abstract: Abstract In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.

Keywords: Robust exponential stability; Nonlinear system; Lyapunov functional; Markovian jump parameter; Mixed time delay (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-9997-5

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