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**Network-based robust \(H_{\infty}\) filtering for the uncertain systems with sensor failures and noise disturbance.**
*(English)*
Zbl 1264.93051

Summary: The network-based robust \(H_{\infty}\) filtering for the uncertain system with sensor failures and the noise is considered in this paper. The uncertain system under consideration is also subject to parameter uncertainties and delay varying in an interval. Sufficient conditions are derived for a linear filter such that the filtering error systems are robust globally asymptotically stable while the disturbance rejection attenuation is constrained to a given level by means of the \(H_{\infty}\) performance index. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is then given for the desired filter parameters. Two numerical examples are exploited to show the usefulness and effectiveness of the proposed filter design method.

### MSC:

93B36 | \(H^\infty\)-control |

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

93B07 | Observability |

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\textit{M. Hua} et al., Math. Probl. Eng. 2012, Article ID 945271, 19 p. (2012; Zbl 1264.93051)

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### References:

[1] | J. Hespanha, P. Naghshtabrizi, and Y. Xu, “A survey of recent results in networked control systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 138-162, 2007. |

[2] | T. Yang, “Networked control system: a brief survey,” IEE Proceedings Control Theory and Applications, vol. 153, no. 4, pp. 403-412, 2006. |

[3] | X. Tang and J. Yu, “Networked control system: survey and directions,” in Proceedings of the Life system modeling and simulation 2007 international conference on Bio-Inspired computational intelligence and applications(LSMS’07), pp. 473-481, 2007. |

[4] | R. Yang, P. Shi, and G.-P. Liu, “Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2655-2660, 2011. · Zbl 1368.93734 |

[5] | H. Song, L. Yu, and W. A. Zhang, “Networked H\infty filtering for linear discrete-time systems,” Information Sciences, vol. 181, no. 3, pp. 686-696, 2011. · Zbl 1205.93096 |

[6] | H. Zhang, Y. Shi, and A. Saadat Mehr, “Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data,” IET Control Theory & Applications, vol. 4, no. 12, pp. 2921-2936, 2010. |

[7] | B. Zhang and W. Zheng, “H\infty filter design for nonlinear networked control systems with uncertain packet-loss proba-bility,” Signal Processing, vol. 92, no. 6, pp. 1499-1507, 2012. |

[8] | W. A. Zhang, L. Yu, and H. Song, “H\infty filtering of networked discrete-time systems with random packet losses,” Information Sciences, vol. 179, no. 22, pp. 3944-3955, 2009. · Zbl 1187.93132 |

[9] | B. Jiang, Z. Mao, and P. Shi, “H\infty -filter design for a class of networked control systems via T-S fuzzy-model approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 1, pp. 201-208, 2010. |

[10] | H. Dong, Z. Wang, and H. Gao, “Robust H\infty filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts,” IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 1957-1966, 2010. · Zbl 1392.94183 |

[11] | A. Tellili, M. N. Abdelkrim, and M. Benrejeb, “Reliable H\infty control of multiple time scales singularly perturbed systems with sensor failure,” International Journal of Control, vol. 80, no. 5, pp. 659-665, 2007. · Zbl 1162.93335 |

[12] | Z. Gao, T. Breikin, and H. Wang, “Reliable observer-based control against sensor failures for systems with time delays in both state and input,” IEEE Transactions on Systems, Man and Cybernetics A, vol. 38, no. 5, pp. 1018-1029. |

[13] | X. He, Z. Wang, and D. Zhou. “Robust H\infty filtering for time-delay systems with probabilistic sensor faults,” IEEE Signal Processing Letters, vol. 16, no. 5, pp. 442-445, 2009. |

[14] | Y. Wang, Y. Zeng, Z. Zuo, and G. Zhang, “Robust output feedback controller design for uncertain delayed systems with sensor failure,” in Proceedings of the 21th Chinese Control and Decision Conference (CCDC ’09), pp. 4122-4127, June 2009. |

[15] | S. Tong, G. Yang, and W. Zhang, “Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays,” International Journal of Applied Mathematics and Computer Science, vol. 21, no. 4, pp. 617-627, 2011. · Zbl 1283.93166 |

[16] | H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Robust H\infty filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 59, no. 7, pp. 3048-3057, 2011. · Zbl 1391.93234 |

[17] | H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Variance-constrained H\infty filtering for a class of nonlinear time-varying systems with multiple missing measurements: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 58, no. 5, pp. 2534-2543, 2010. · Zbl 1391.93233 |

[18] | B. Shen, Z. Wang, and X. Liu, “A stochastic sampled-data approach to distributed H\infty filtering in sensor networks,” IEEE Transactions on Circuits and Systems, vol. 58, no. 9, pp. 2237-2246, 2011. |

[19] | B. Zhang, W. X. Zheng, and S. Xu, “On robust H\infty filtering of uncertain Markovian jump time-delay systems,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 2, pp. 138-157, 2012. · Zbl 1417.93318 |

[20] | E. Tian, D. Yue, T. Yang, Z. Gu, and G. Lu, “T-S fuzzy model-based robust stabilization for networked control systems with probabilistic sensor and actuator failure,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 3, pp. 553-561, 2011. |

[21] | X. Zhao, E. Tian, J. Wei, and Y. Yuan, “Reliable H\infty filter design for nonlinear networked control systems with probabilistic sensor failure,” in Proceedings of the 30th Chinese Control Conference, pp. 4170-4175, 2011. |

[22] | L. Du, Z. Gu, and J. Liu, “Network-based reliable H\infty filter designing for the systems with sensor failures,” in Proceedings of the International Conference on Modelling, Identification and Control, pp. 17-19, Okayama, Japan, July 2010. |

[23] | H. Shao, “New delay-dependent stability criteria for systems with interval delay,” Automatica, vol. 45, no. 3, pp. 744-749, 2009. · Zbl 1168.93387 |

[24] | S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004 |

[25] | K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston, Mass, USA, 2003. · Zbl 1039.34067 |

[26] | Y. Y. Wang, L. Xie, and C. E. de Souza, “Robust control of a class of uncertain nonlinear systems,” Systems & Control Letters, vol. 19, no. 2, pp. 139-149, 1992. · Zbl 0765.93015 |

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