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**Stability criteria for uncertain stochastic dynamic systems with time-varying delays.**
*(English)*
Zbl 1213.93201

Summary: The problem of delay-dependent stability for uncertain stochastic dynamic systems with time-varying delay is considered. Based on the Lyapunov stability theory, improved delay-dependent stability criteria for the system are established in terms of linear matrix inequalities. Three numerical examples are given to show the effectiveness of the proposed method.

### MSC:

93E15 | Stochastic stability in control theory |

93E03 | Stochastic systems in control theory (general) |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

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\textit{O. M. Kwon}, Int. J. Robust Nonlinear Control 21, No. 3, 338--350 (2011; Zbl 1213.93201)

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### References:

[1] | Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002 |

[2] | Kolmanovskii, Applied Theory of Functional Differential Equations (1992) · Zbl 0840.34084 |

[3] | Kwon, On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays, Applied Mathematics and Computation 197 pp 864– (2009) · Zbl 1144.34052 |

[4] | Kwon, On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations, Applied Mathematics and Computation 203 pp 937– (2008) · Zbl 1168.34354 |

[5] | Park, Delay-dependent guaranteed cost stabilization criterion for neutral-delay-differential systems: matrix inequality approach, Computers and Mathematics with Applications 47 pp 1507– (2004) · Zbl 1070.34106 |

[6] | Cao, Boundedness and stability for Cohen-Grossberg neural network with time-varying delays, Journal of Mathematical Analysis and Applications 296 pp 665– (2004) · Zbl 1044.92001 |

[7] | Kwon, On improved delay-dependent stability criterion of certain neutral differential equations, Applied Mathematics and Computation 199 pp 385– (2008) · Zbl 1146.34328 |

[8] | Li, Delay-range-dependent robust stability and stabilization for uncertain systems with time-varying delay, International Journal of Robust and Nonlinear Control 18 pp 1372– (2008) · Zbl 1298.93263 |

[9] | Yue, Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties, Electronics Letters 37 pp 992– (2001) · Zbl 1190.93095 |

[10] | Xu, A new LMI condition for delay dependent robust stability of stochastic time-delay systems, Asian Journal of Control 7 pp 419– (2005) |

[11] | Yang, New delay-dependent stability criterion for stochastic systems with time delays, IET Control Theory and Applications 2 pp 966– (2008) |

[12] | Yan, Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay, Chaos Solitons Fractals 40 pp 1668– (2009) · Zbl 1198.93171 |

[13] | Gu K An integral inequality in the stability problem of time-delay systems 2805 2810 |

[14] | Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 |

[15] | Khasminskii, Stochastic Stability of Differential Equations (1980) · Zbl 1259.60058 |

[16] | Arnold, Stochastic Differential Equations: Theory and Applications (1972) |

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