Robust exponential stability for uncertain time-varying delay systems with delay dependence.

*(English)*Zbl 1192.34086Summary: This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov-Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.

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\textit{P.-L. Liu}, J. Franklin Inst. 346, No. 10, 958--968 (2009; Zbl 1192.34086)

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[1] | Boyd, S.L.; Feron, G.E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA |

[2] | Cao, Y.Y.; Lem, J., Computation of robust stability bounds for time delay systems with nonlinear time-varying perturbations, International journal of systems science, 31, 359-365, (2000) · Zbl 1080.93519 |

[3] | Y. Chen, A. Xue, R.Q. Lu, J.H. Wang, On delay-dependent robust stability for uncertain systems with time-varying delays, in: Sixteenth IEEE International Conference on Control Applications Part of IEEE Multi-conference on Systems and Control Singapore, 2007, pp. 1561-1564. |

[4] | Fridman, E.; Shaked, U., An improvement stabilization method for linear time delay systems, IEEE transactions on automatic control, 47, 1931-1937, (2002) · Zbl 1364.93564 |

[5] | Han, Q.L., Robust stability for a class of linear systems with time-varying delay and nonlinear perturbations, Computers and mathematics with applications, 47, 1201-1209, (2004) · Zbl 1154.93408 |

[6] | Kim, J.H., Delay and its time-derivative delay robust stability of time-delayed linear systems with uncertainty, IEEE transactions on automatic control, 46, 789-792, (2001) · Zbl 1008.93056 |

[7] | Kwon, O.M.; Park, J.H., Exponential stability of uncertain dynamic systems including state delay, Applied mathematics letters, 19, 901-907, (2006) · Zbl 1220.34095 |

[8] | Li, X.; De Souza, C.E., Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach, IEEE transactions on automatic control, 42, 1144-1148, (1997) · Zbl 0889.93050 |

[9] | F.G. Li, X.P. Guan, Delay-dependent stability for time-delay systems with nonlinear perturbations, in: Proceedings of the Sixth World Congress on Intelligent Control and Automation, Dalian, China, 2006, pp. 311-313. |

[10] | Liu, P.L., Exponential stability for linear time-delay systems with delay-dependence, Journal of the franklin institute, 340, 481-488, (2003) · Zbl 1035.93060 |

[11] | Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain stated-delayed systems, International journal of control, 74, 1447-1451, (2001) |

[12] | Mori, T.; Fukuma, N.; Kuwalhara, M., A way to stabilized linear systems with delayed state, IEEE transactions on automatic control, 19, 571-573, (1983) · Zbl 0544.93055 |

[13] | M.N.A. Parlakic, Robust stability of uncertain time-varying state-delayed systems, in: Proceedings of the 2006 American Control Conference Minneapolis, MN, USA, 2006, pp. 1529-1534. |

[14] | Su, T.J.; Lu, C.Y.; Tsai, J.S.H., LMI approach to delay-dependent robust stability for uncertain time-delay systems, IEE proceedings—control theory and applications, 148, 209-212, (2001) |

[15] | Wu, M.; Yong, H.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-2439, (2004) · Zbl 1059.93108 |

[16] | Yue, D.; Won, S., An improvement on ‘delay and its time-derivative delay robust stability of time-delayed linear systems with uncertainty’, IEEE transactions on automatic control, 47, 407-408, (2002) · Zbl 1364.93609 |

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