This study is concerned with the problem of robust reliable dissipative filter design for networked control systems (NCSs) with sensor failures and random packet dropouts. The considered NCS model is subject to the sources of uncertainty in the system parameters. The sensor signals are modelled by sequences of a Bernoulli distributed white sequence and the packet dropouts may occur randomly during transmission. The main objective is to design a suitable reliable dissipative filter such that, for all network-induced imperfections, a resulting error system is robustly stochastically stable and strictly (𝒬, 𝒮, ℛ) dissipative. The results are obtained for known as well as unknown sensor failure rates, so the results are more general one because it can guarantee the dissipativity of system whether or not the sensor encounter failures. The sufficient conditions for existence of filters are derived in terms of linear matrix inequality (LMI) approach and the corresponding filter parameters can be obtained by solution to a set of LMIs, which can be easily solved by using some standard numerical packages. Finally, two numerical examples are given to illustrate the applicability and effectiveness of the proposed filter design.

References

1. 1)
  - 18. Zhu, C., Xia, Y., Xie, L., et al: ‘Optimal linear estimation for systems with transmission delays and packet dropouts’, IET Signal Process., 2013, 7, (9), pp. 814–823 (doi: 10.1049/iet-spr.2012.0348).
2. 2)
  - 2. Liu, J., Wang, J., Yang, G.: ‘Reliable guaranteed variance filtering against sensor failures’, IEEE Trans. Signal Process., 2003, 51, (37), pp. 1403–1411.
3. 3)
  - L. Xie . Output feedback H∞ control of systems with parameter uncertainty. Int. J. Control , 4 , 741 - 750
4. 4)
  - M. Sahebsara , T. Chen , S.L. Shah . Optimal H2 filtering with random sensor delay, multiple packet dropouts and uncertain observations. Int. J. Control , 292 - 301
5. 5)
  - 9. Balasubramaniam, P., Revathi, V.M., Park, J.H.: ‘L2 − L∞ filtering for neutral Markovian switching system with mode-dependent time-varying delays and partially unknown transition probabilities’, Appl. Math. Comput., 2013, 219, (17), pp. 9524–9542 (doi: 10.1016/j.amc.2013.03.037).
6. 6)
  - 26. Chen, B., Zhang, W.A., Yu, L.: ‘Distributed finite-horizon fusion Kalman filtering for bandwidth and energy constrained wireless sensor networks’, IEEE Trans. Signal Process., 2014, 62, (4), pp. 797–812, (doi: 10.1109/TSP.2013.2294603).
7. 7)
  - J.C. Willems . Dissipative dynamical systems – part I: general theory. Arch. Ration. Mech. Anal. , 321 - 351
8. 8)
  - 10. Chen, B., Yu, L., Zhang, W., Liu, A.: ‘Robust information fusion estimator for multiple delay-tolerant sensors with different failure rates’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2013, 60, (2), pp. 401–414 (doi: 10.1109/TCSI.2012.2215801).
9. 9)
  - 13. Wu, Z., Park, J.H., Su, H., et al: ‘Mixed ℋ∞ and passive filtering for singular systems with time delays’, Signal Process., 2013, 93, (7), pp. 1705–1711 (doi: 10.1016/j.sigpro.2013.01.003).
10. 10)
  - 23. Zhang, B., Zheng, W.: ‘H∞ filter design for nonlinear networked control systems with uncertain packet-loss probability’, Signal Process., 2012, 92, pp. 1499–1507 (doi: 10.1016/j.sigpro.2011.12.010).
11. 11)
  - 40. Liu, B., Liu, X., Teo, K.L.: ‘Feedback stabilization of dissipative impulsive dynamical systems’, Inf. Sci., 2007, 177, (7), pp. 1663–1672 (doi: 10.1016/j.ins.2006.09.019).
12. 12)
  - 10. Song, Y., Wang, J., Shi, Y., Li, C.: ‘H∞ control of networked control systems with time delay and packet disordering’, J. Franklin Inst., 2013, 350, (6), pp. 1596–1616 (doi: 10.1016/j.jfranklin.2013.02.006).
13. 13)
  - 7. Aguila, R.C., Carazo, A.H., Perez, J.L.: ‘Covariance-based estimation algorithms in networked systems with mixed uncertainties in the observations’, Signal Process., 2014, 94, pp. 163–173 (doi: 10.1016/j.sigpro.2013.06.035).
14. 14)
  - 7. Wu, Z., Cui, M., Xie, X., et al: ‘Theory of stochastic dissipative systems’, IEEE Trans. Autom. Control, 2011, 56, (7), pp. 1650–1655 (doi: 10.1109/TAC.2011.2121370).
15. 15)
  - 27. Li, H., Yang, H., Sun, F., Xia, Y.: ‘A network-bound-dependent stabilization method of networked control systems’, Automatica, 2013, 49, pp. 2561–2566 (doi: 10.1016/j.automatica.2013.04.032).
16. 16)
  - 46. Wang, Z., Shu, H., Fang, J., et al: ‘Robust stability for stochastic Hopfield neural networks with time delays’, Nonlinear Anal. Real World Appl., 2006, 7, (5), pp. 1119–1128 (doi: 10.1016/j.nonrwa.2005.10.004).
17. 17)
  - 6. Yang, G., Ye, D.: ‘Adaptive reliable ℋ∞ filtering against sensor failures’, IEEE Trans. Signal Process., 2007, 55, (7), pp. 3161–3171 (doi: 10.1109/TSP.2007.893906).
18. 18)
  - 38. Dong, X.: ‘Robust strictly dissipative control for discrete singular systems’, IET Control Theory Appl., 2007, 1, (4), pp. 1060–1067 (doi: 10.1049/iet-cta:20060173).
19. 19)
  - 24. Vesely, V., Rosinova, D., Quang, T.N.: ‘Networked output feedback robust predictive controller design’, Int. J. Innov. Comput. I, 2013, 9, (10), pp. 3941–3953.
20. 20)
  - 3. Liu, Y., Wang, Z., Wang, W.: ‘Reliable ℋ∞ filtering for discrete time-delay systems with randomly occurred nonlinearities via delay partitioning method’, Signal Process., 2011, 91, (4), pp. 713–727 (doi: 10.1016/j.sigpro.2010.07.018).
21. 21)
  - 29. Qiu, L., Luo, Q., Gong, F., et al: ‘Stability and stabilization of networked control systems with random time delays and packet dropouts’, J. Frankl. Inst., 2013, 350, (7), pp. 1886–1907 (doi: 10.1016/j.jfranklin.2013.05.013).
22. 22)
  - 6. Liu, M., Wang, Q., Li, H.: ‘State estimation and stabilization for nonlinear networked control systems with limited capacity channel’, J. Frankl. Inst., 2011, 348, (8), pp. 1869–1885 (doi: 10.1016/j.jfranklin.2011.05.008).
23. 23)
  - 28. Moarref, M., Rodrigues, L.: ‘On exponential stability of linear networked control systems’, Int. J. Robust Nonlinear Control, 2012, doi: 10.1002/rnc.2936.
24. 24)
  - 19. Mahmoud, M.S., Selim, S.Z., Shi, P., et al: ‘New results on networked control systems with non-stationary packet dropouts’, IET Control Theory Appl., 2012, 6, (15), pp. 2442–2452 (doi: 10.1049/iet-cta.2012.0487).
25. 25)
  - 5. He, X., Wang, Z., Ji, Y., et al: ‘State estimation for networked systems with randomly occurring quantisations’, Int. J. Syst. Sci., 2013, 44, (7), pp. 1253–1263. (doi: 10.1080/00207721.2012.702245).
26. 26)
  - 44. Zhang, W.A., Yu, L., Song, H.: ‘ℋ∞ filtering of networked discrete-time systems with random packet losses’, Inf. Sci., 2009, 179, (22), pp. 3944–3955 (doi: 10.1016/j.ins.2009.07.016).
27. 27)
  - 25. Yang, X., Hua, C., Yan, J., et al: ‘New stability criteria for networked teleoperation system’, Inf. Sci., 2013, 233, pp. 244–254 (doi: 10.1016/j.ins.2013.01.016).
28. 28)
  - 22. Yang, R., Liu, G.P., Shi, P., Thomas, C., Basin, M.: ‘Predictive output feedback control for networked control systems’, IEEE Trans. Ind. Electron., 2014, 61, (1), pp. 512–520 (doi: 10.1109/TIE.2013.2248339).
29. 29)
  - 14. Hmamed, A., Kasri, C.E., Tissir, E.H., et al: ‘Robust ℋ∞ filtering for uncertain 2-D continuous systems with delays’, Int. J. Innov. Comput. I, 2013, 9, (5), pp. 2167–2183.
30. 30)
  - 1. Guo, X., Yang, G.: ‘Reliable ℋ∞ filter design for discrete time systems with sector-bounded nonlinearities: an LMI optimization’, Acta Autom. Sin., 2009, 35, (10), pp. 1347–1351 (doi: 10.3724/SP.J.1004.2009.01347).
31. 31)
  - 8. Li, W., Xu, Y., Li, H.: ‘Robust l2–l∞ filtering for discrete-time Markovian jump linear systems with multiple sensor faults, uncertain transition probabilities and time-varying delays’, IET Signal Process., 2013, 7, (8), pp. 710–719 (doi: 10.1049/iet-spr.2012.0325).
32. 32)
  - 29. Liu, Y., Wang, Z., Wang, W.: ‘Robust reliable control for discrete-time-delay systems with stochastic nonlinearities and multiplicative noises’, Opt. Control Appl. Methods, 2011, 32, (3), pp. 285–297 (doi: 10.1002/oca.938).
33. 33)
  - 21. Wang, J., Liu, C., Yang, H.: ‘Stability of a class of networked control systems with Markovian characterization’, Appl. Math. Model., 2012, 36, (7), pp. 3168–3175 (doi: 10.1016/j.apm.2011.10.010).
34. 34)
  - 16. Wen, S., Zeng, Z., Huang, T.: ‘Reliable ℋ∞ filtering for neutral systems with mixed delays and multiplicative noises’, Signal Process., 2014, 94, pp. 23–32 (doi: 10.1016/j.sigpro.2013.06.002).
35. 35)
  - 8. Liu, J., Yue, D., Gu, Z., et al: ‘ℋ∞ filtering for systems with time-varying delay satisfying a certain stochastic characteristic’, IET Signal Process., 2011, 5, (8), pp. 757–766 (doi: 10.1049/iet-spr.2010.0119).
36. 36)
  - 15. Chen, B., Yu, L., Zhang, W.A., Wang, H.: ‘Distributed ℋ∞ fusion filtering with communication bandwidth constraints’, Signal Process., 2014, 96B, pp. 284–289 (doi: 10.1016/j.sigpro.2013.09.015).
37. 37)
  - X. He , Z. Wang , D. Zhou . Robust h-infinity filtering for time-delay systems with probabilistic sensor faults. IEEE Signal Process. Lett. , 5 , 442 - 445
38. 38)
  - 42. Feng, Z., Lam, J.: ‘Robust reliable dissipative filtering for discrete delay singular systems’, Signal Process., 2012, 92, (12), pp. 3010–3025 (doi: 10.1016/j.sigpro.2012.06.003).
39. 39)
  - 41. Wang, J., Park, J.H., Shen, H., et al: ‘Delay-dependent robust dissipativity conditions for delayed neural networks with random uncertainties’, Appl. Math. Comput., 2013, 221, pp. 710–719 (doi: 10.1016/j.amc.2013.07.017).
40. 40)
  - 30. Yang, F., Han, Q.L.: ‘ℋ∞control for networked systems with multiple packet dropouts’, Inf. Sci., 2013, 252, pp. 106–117 (doi: 10.1016/j.ins.2013.06.043).
41. 41)
  - P. Park , J.W. Ko , C. Jeong . Reciprocally convex approach to stability of systems with time-varying delays. Automatica , 1 , 235 - 238
42. 42)
  - 32. Zhao, X., Tian, E.: ‘Novel criteria on ℋ∞ filter design of linear networked control systems’, IET Signal Process., 2013, 7, (1), pp. 1–13 (doi: 10.1049/iet-spr.2012.0041).
43. 43)
  - 34. Zhou, S., Feng, G.: ‘ℋ∞ filtering for discrete-time systems with randomly varying sensor delays’, Automatica, 2008, 44, (7), pp. 1918–1922 (doi: 10.1016/j.automatica.2007.10.026).
44. 44)
  - 47. Gao, H.J., Lam, J., Chen, T.W., Wang, C.H.: ‘Feedback control with signal transmission after-effects’, Int. J. Robust Nonlinear Control, 2008, 18, (3), pp. 351–363 (doi: 10.1002/rnc.1233).
45. 45)
  - R. Yang , P. Shi , G. Li . Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Trans. Autom. Control , 2655 - 2660
46. 46)
  - 39. Li, Z., Wang, J., Shao, H.: ‘Delay-dependent dissipative control for linear time-delay systems’, J. Frankl. Inst., 2002, 339, (6–7), pp. 529–542 (doi: 10.1016/S0016-0032(02)00030-3).
47. 47)
  - 10. Chen, H.: ‘Delay-dependent robust ℋ∞ filter design for uncertain neutral stochastic system with time-varying delay’, IET Signal Process., 2013, 7, (5), pp. 368–381 (doi: 10.1049/iet-spr.2012.0112).
48. 48)
  - 31. Zhang, Y., Liu, Z., Fang, H., et al: ‘ℋ∞ fault detection for nonlinear networked systems with multiple channels data transmission pattern’, Inf. Sci., 2013, 221, pp. 534–543 (doi: 10.1016/j.ins.2012.09.026).

Robust reliable dissipative filtering for networked control systems with sensor failure

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