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Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

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  • Gao, Huijun
  • Lam, James
  • Wang, Zidong

Abstract

This paper deals with the problems of stability analysis and static output-feedback stabilization for discrete stochastic systems with time-varying state delay. A delay-dependent condition for mean-square asymptotic stability is first established in terms of linear matrix inequalities (LMIs), which can be solved efficiently via available numerical software. Connection with an existing result on related topics is thoroughly discussed. Based on the established stability criterion, the problem of static output-feedback stabilization is then investigated, which is cast into a nonlinear minimization problem involving LMI constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) is proposed to solve the nonlinear minimization problem. A numerical example is provided to demonstrate the feasibility and applicability of the proposed approaches.

Suggested Citation

  • Gao, Huijun & Lam, James & Wang, Zidong, 2007. "Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 394-404.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:394-404
    DOI: 10.1016/j.chaos.2006.03.027
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    References listed on IDEAS

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    1. He, Yong & Wang, Qing-Guo & Zheng, Wei-Xing, 2005. "Global robust stability for delayed neural networks with polytopic type uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1349-1354.
    2. Shu, Huisheng & Wei, Guoliang, 2005. "H∞ analysis of nonlinear stochastic time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 637-647.
    3. Lin, Chong & Wang, Qing-Guo & Lee, Tong Heng, 2006. "Less conservative stability conditions for fuzzy large-scale systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1147-1154.
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    1. Xiaofeng Li & Weiqun Wang & Lizhen Li, 2015. "control for 2-D T-S fuzzy FMII model with stochastic perturbation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 609-624, March.
    2. Yue, Dong & Lam, James & Wang, Zidong, 2009. "Persistent disturbance rejection via state feedback for networked control systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 382-391.
    3. Li, Ping & Zhong, Shou-ming & Cui, Jin-zhong, 2009. "Delay-dependent robust BIBO stabilization of uncertain system via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1021-1028.
    4. Karimi, Hamid Reza & Maass, Peter, 2009. "Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1125-1135.

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