##
**Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay.**
*(English)*
Zbl 1217.93178

Summary: A nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.

### MSC:

93E15 | Stochastic stability in control theory |

93C55 | Discrete-time control/observation systems |

93D15 | Stabilization of systems by feedback |

### Keywords:

nonlinear networked control systems; random packet dropout; time-varying delay; stochastic stabilization; linear matrix inequality
PDFBibTeX
XMLCite

\textit{Y. Zhang} and \textit{H. Fang}, Appl. Math. Modelling 35, No. 5, 2253--2264 (2011; Zbl 1217.93178)

Full Text:
DOI

### References:

[1] | Hespanha, J.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems, IEEE Proc., 95, 138-162 (2007) |

[2] | Nilsson, J.; Bernhardsson, B.; Wittenmark, B., Stochastic analysis and control of real-time systems with random time delays, Automatica, 34, 57-64 (1998) · Zbl 0908.93073 |

[3] | Kim, D.; Lee, Y.; Kwon, W.; Park, H., Maximum allowable delay bounds of networked control systems, Control Eng. Pract., 11, 1301-1313 (2003) |

[4] | Zheng, Y.; Fang, H. J.; Wang, H. O., Takagi-sugeno fuzzy-model-based fault detection for networked control systems with Markov delays, IEEE Trans. Syst. Man Cybern. Part B, 36, 924-929 (2006) |

[5] | Xiong, J. L.; Lam, J., Stabilization of networked control systems with a logic ZOH, IEEE Trans. Automat. Control, 54, 358-363 (2009) · Zbl 1367.93546 |

[6] | Yang, F. W.; Wang, Z. D.; Hung, Y. S.; Gani, M., \(H\)∞ control for networked systems with random communication delays, IEEE Trans. Automat. Control, 51, 511-518 (2006) · Zbl 1366.93167 |

[7] | Wang, Z.; Yang, F.; Ho, D. W.C.; Liu, X., Robust \(H\)∞ control or networked systems with random packet losses, IEEE Trans. Syst. Man Cybern. Part B, 37, 916-924 (2007) |

[8] | Sahebsara, M.; Chen, T. W.; LShah, S., Optimal \(H\)∞ filtering in networked control systems with multiple packet dropouts, Syst. Control Lett., 57, 696-702 (2008) · Zbl 1153.93034 |

[9] | Fang, X.; Wang, J., Stochastic observer-based guaranteed cost control for networked control systems with packet dropouts, IET Control Theory Appl., 2, 980-989 (2008) |

[10] | Yue, D.; Han, Q. L.; Lam, J., Network-based robust \(H\)∞ control of systems with uncertainty, Automatica, 41, 999-1007 (2005) · Zbl 1091.93007 |

[11] | Yu, M.; Wang, L.; Chu, T.; Xie, G., Stabilization of networked control systems with data packet dropout and network delays via switching system approach, Proc. CDC, 3539-3544 (2004) |

[12] | Zhang, W. A.; Yu, L., Modelling and control of networked control systems with both network-induced delay and packet-dropout, Automatica, 44, 3206-3210 (2008) · Zbl 1153.93321 |

[13] | Han, Q. L., Absolute stability for time delay systems with sector-bound nonlinearity, Automatica, 41, 2171-2176 (2005) · Zbl 1100.93519 |

[14] | Sun, J.; Liu, G. P., State feedback and output feedback control of a class of nonlinear systems with delayed measurements, Nonlinear Anal., 67, 1623-1636 (2007) · Zbl 1123.34064 |

[15] | Kwon, O. M.; Park, J. H.; Lee, S. M., On robust stability criteria for dynamic systems with time-varying delays and nonlinear perturbations, Appl. Math. Comput., 203, 937-942 (2008) · Zbl 1168.34354 |

[16] | Qiu, F.; Cui, B. T.; Ji, Y., Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations, Nonlinear Anal.: Real World Appl., 11, 895-906 (2010) · Zbl 1187.37124 |

[17] | Peng, C.; Tian, Y. C.; Tade, M. O., State feedback controller design of networked control systems with interval time-varying delay and nonlinearity, Int. J. Robust Nonlinear Control, 18, 1285-1301 (2008) · Zbl 1284.93111 |

[18] | Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE Trans. Automat. Control, 44, 876-877 (1999) · Zbl 0957.34069 |

[19] | Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. Control, 74, 447-1455 (2001) · Zbl 1023.93055 |

[20] | He, Y.; Liu, G. P.; Rees, D.; Wu, M., \(H\)∞ filtering for discrete-time systems with time-varying delay, Signal Process., 89, 275-282 (2009) · Zbl 1151.94369 |

[21] | Zhang, X. M.; Han, Q. L., Delay-dependent robust \(H\)∞ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality, IEEE Trans. Circuits Syst. II, 58, 1466-1470 (2006) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.