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Delay-Range-Dependent Stability for Stochastic Systems with Time-Varying Delay

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 287)

Abstract

This paper is concerned with the stability analysis for stochastic systems with time-varying delay in a range. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay.

Keywords

Delay-range-dependent Stochastic systems Linear matrix inequality (LMI) Stability 

References

  1. 1.
    He Y et al (2007) Delay-range-dependent stability for systems with time-varying delay. Automatica 43(2):371–376CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Balasubramaniam P, Krishnasamy R, Rakkiyappan R (2012) Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays. Commun Nonlinear Sci Numer Simul 17(9):3612–3627CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Sun J et al (2010) Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2):466–470CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Song B et al (2013) New results on delay-dependent stability analysis for neutral stochastic delaysystems. J Franklin Inst 350(4):840–852Google Scholar
  5. 5.
    Xu S et al (2002) Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans Autom Control 47(7):1122–1128CrossRefGoogle Scholar
  6. 6.
    Xie S, Xie L (2000) Stabilization of a class of uncertain large-scale stochastic systems with time delays. Automatica 36(1):161–167CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Xu SY, Chen TW (2002) Robust H-infinity control for uncertain stochastic systems with state delay. IEEE Trans Autom Control 47(12):2089–2094CrossRefGoogle Scholar
  8. 8.
    Zhao X et al (2012) Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans Autom Control 57(7):1809–1815CrossRefGoogle Scholar
  9. 9.
    Kolmanovskii V, Myshkis A (1999) Introduction to the theory and applications of functional differential equations, vol 463, SpringerGoogle Scholar
  10. 10.
    Mao X, Koroleva N, Rodkina A (1998) Robust stability of uncertain stochastic differential delay equations. Syst Control Lett 35(5):325–336CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Hale JK (1993) Introduction to functional differential equations, vol 99, SpringerGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Electrical Engineering and AutomationQilu University of TechnologyJinanChina

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