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A Survey on Filtering Issues for Two-Dimensional Systems: Advances and Challenges

  • Control Theory and Applications
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Abstract

In the past few decades, both theoretical developments and practical applications of the two-dimensional (2-D) systems have received considerable research interest due to their clear engineering insights in many industrial branches. In order to estimate the actual system states from available and possibly noisy measurements, various filtering strategies have been proposed in the existing literature which include, but are not limited to, Kalman filtering, variance-constrained filtering, H∞ filtering, l2-l∞ filtering, l1 filtering, dissipative filtering, and protocol-based filtering approaches. In particular, the filtering issues of 2-D systems subjected to disturbances/noises from different sources have drawn much research attention. The intent of this survey is to not only provide a comprehensive review of the latest results but also bestow some in-depth insights on the future research with respect to the filter design problems for 2-D systems under various performance requirements. The fundamentals of the 2-D systems are first presented and the corresponding filtering techniques are introduced from the aspects of engineering insights and physical interpretations. Then, several well-known 2-D systems are recalled and discussed, and some other 2-D systems with more complicated dynamics are surveyed. Subsequently, the recent advances in designing appropriate 2-D filtering algorithms under specific filtering performance indices are reviewed. Finally, this paper is concluded with some possible future research topics outlined on the 2-D filtering schemes.

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References

  1. N. K. Bose, Multidimensional Systems Theory and Applications, Kluwer Academic Publisher, The Netherlands, 2003.

    Google Scholar 

  2. T. Kaczorek, Two-Dimensional Linear Systems, Springer-Verlag, Berlin, 1985.

    MATH  Google Scholar 

  3. P. Pakshin, J. Emelianova, M. Emelianov, K. Galkowski, and E. Rogers, “Dissipativity and stabilization of nonlinear repetitive processes,” Systems & Control Letters, vol. 91, pp. 14–20, 2016..

    Article  MathSciNet  MATH  Google Scholar 

  4. E. Fornasini and G. Marchesini, “State-space realization theory of two-dimensional filters,” IEEE Transactions on Automatic Control, vol. AC-21, no. 4, pp. 484–492, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. Fornasini and G. Marchesini, “Doubly-indexed dynamical systems: state-space models and structural properties,” Mathematical Systems Theory, vol. 12, no. 1, pp. 59–72, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. D. Givone and R. P. Roesser, “Multidimensional linear iterative circuits general properties,” IEEE Transactions on Computers, vol. C-21, no. 10, pp. 1067–1073, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Yalcin, R. Collins, and M. Hebert, “Background estimation under rapid gain change in thermal imagery,” Computer Vision and Image Understanding, vol. 106, nos. 2–3, pp. 148–161, 2007.

    Article  Google Scholar 

  8. C. K. Ahn, P. Shi, and M. V. Basin, “Two-dimensional dissipative control and filtering for Roesser model,” IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1745–1759, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Chen, C. Zhao, J. Lam, Y. Cui, and K.-W. Kwok, “Stability and l1-gain analysis for positive 2-D Markov jump systems,” International Journal of Systems Science, vol. 50, no. 11, pp. 2077–2087, 2019.

    Article  MathSciNet  Google Scholar 

  10. C. Du, L. Xie, and C. Zhang, “H∞ control and robust stabilization of two-dimensional systems in Roesser models,” Automatica, vol. 37, no. 2, pp. 205–211, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Gao, J. Lam, C. Wang, and S. Xu, “H∞ model reduction for uncertain two-dimensional discrete systems,” Optimal Control Applications and Methods, vol. 26, no. 4, pp. 199–227, 2005.

    Article  MathSciNet  Google Scholar 

  12. S. Rathinasamy, H. R. Karimi, K. Raajananthini, P. Selvaraj, and Y. Ren, “Observer-based tracking control for switched stochastic systems based on a hybrid 2-D model,” International Journal of Robust and Nonlinear Control, vol. 28, no. 2, pp. 478–491, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. Wang, D. Zhao, Y. Li, and S. X. Ding, “Unbiased minimum variance fault and state estimation for linear discrete time-varying two-dimensional systems,” IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 5463–5469, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  14. Z.-G. Wu, Y. Shen, P. Shi, Z. Shu, and H. Su, “H∞ control for 2-D Markov jump systems in Roesser model,” IEEE Transactions on Automatic Control, vol. 64, no. 1, pp. 427–432, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  15. R. Yang, L. Xie, and C. Zhang, “H2 and mixed H2/H∞ control of two-dimensional systems in Roesser model,” Automatica, vol. 42, no. 9, pp. 1507–1514, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Abedor, K. Nagpal, and K. Poolla, “A linear matrix inequality approach to peak-to-peak gain minimization,” International Journal of Robust and Nonlinear Control, vol. 6, no. 9–10, pp. 899–927, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  17. X.-H. Chang and Y.-M. Wang, “Peak-to-peak filtering for networked nonlinear DC motor systems with quantization,” IEEE Transactions on Industrial Informatics, vol. 14, no. 12, pp. 5378–5388, 2018.

    Article  Google Scholar 

  18. S. He and F. Liu, “Robust peak-to-peak filtering for Markov jump systems,” Signal Processing, vol. 90, no. 2, pp. 513–522, 2010.

    Article  MATH  Google Scholar 

  19. J. Hu, Z. Wang, G.-P. Liu, and H. Zhang, “Variance-constrained recursive state estimation for time-varying complex networks with quantized measurements and uncertain inner coupling,” IEEE Transactions on Neural Networks and Learning Systems, 2019. DOI: https://doi.org/10.1109/TNNLS.2019.2927554

  20. U. Shaked, L. Xie, and Y. C. Soh, “New approaches to robust minimum variance filter design,” IEEE Transactions on Signal Processing, vol. 49, no. 11, pp. 2620–2629, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Variance-constrained H∞ 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.

    Article  MathSciNet  MATH  Google Scholar 

  22. D. Zhao, S. X. Ding, H. Karimi, and Y. Li, “Robust H∞ filtering for two-dimensional uncertain linear discrete time-varying systems: a Krein space-based method,” IEEE Transactions on Automatic Control, vol. 64, no. 12, pp. 5124–5131, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  23. Y. Zou, M. Sheng, N. Zhong, and S. Xu, “A generalized Kalman filter for 2D discrete systems,” Circuits, Systems and Signal Processing, vol. 23, no. 5, pp. 351–364, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  24. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Transactions of the ASME-Journal of Basic Engineering, vol. 82 (Series D), pp. 35–45, 1960.

    Article  MathSciNet  Google Scholar 

  25. S. O. R. Moheimani, A. V. Savkin, and I. R. Petersen, “Robust filtering, prediction, smoothing, and observability of uncertain systems,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 45, no. 4, pp. 446–457, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  26. W. Li, Y. Jia, and J. Du, “Variance-constrained state estimation for nonlinearly coupled complex networks,” IEEE Transactions on Cybernetics, vol. 48, no. 2, pp. 818–824, 2018.

    Article  Google Scholar 

  27. U. Shaked and C. E. de Souza, “Robust minimum variance filtering,” IEEE Transactions on Signal Processing, vol. 43, no. 11, pp. 2474–2483, 1995.

    Article  Google Scholar 

  28. Y. Theodor and U. Shaked, “Robust discrete-time minimum-variance filtering,” IEEE Transactions on Signal Processing, vol. 44, no. 2, pp. 181–189, 1996.

    Article  Google Scholar 

  29. M. Vidyasagar, “Optimal rejection of persistent bounded disturbances,” IEEE Transactions on Automatic Control, vol. 31, no. 6, pp. 527–534, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  30. P. Shi, X. Su, and F. Li, “Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation,” IEEE Transactions on Automatic Control, vol. 61, no. 6, pp. 1694–1699, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  31. H. Geng, Z. Wang, and Y. Cheng, “Distributed federated Tobit Kalman filter fusion over a packet-delaying network: a probabilistic perspective,” IEEE Transactions on Signal Processing, vol. 66, no. 17, pp. 4477–4489, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  32. D. Nešić and A. R. Teel, “Input-output stability properties of networked control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 10, pp. 1650–1667, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Tabbara and D. Nešić, “Input-output stability of networked control systems with stochastic protocols and channels,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1160–1175, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Walsh, H. Ye, and L. Bushnell, “Stability analysis of networked control systems,” IEEE Transactions on Control Systems Technology, vol. 10, no. 3, pp. 438–446, 2002.

    Article  Google Scholar 

  35. Y. Yuan, Z. Wang, P. Zhang, and H. Liu, “Near-optimal resilient control strategy design for state-saturated networked systems under stochastic communication protocol,” IEEE Transactions on Cybernetics, vol. 49, no. 8, pp. 3155–3167, 2019.

    Article  Google Scholar 

  36. R. Caballero-Águila, A. Hermoso-Carazo, and J. Linares-Pérez, “Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements,” International Journal of General Systems, vol. 44, no. 2, pp. 142–154, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  37. J. Ma and S. Sun, “Optimal linear estimators for systems with random sensor delays, multiple packet dropouts and uncertain observations,” IEEE Transactions on Signal Processing, vol. 59, no. 11, pp. 5181–5192, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  38. L. Ma, Z. Wang, Q.-L. Han, and H.-K. Lam, “Envelope-constrained H∞ filtering for nonlinear systems with quantization effects: the finite horizon case,” Automatica, vol. 93, pp. 527–534, 2018..

    Article  MathSciNet  MATH  Google Scholar 

  39. W. Li, Z. Wang, Q. Liu, and L. Guo, “An information aware event-triggered scheme for particle filter based remote state estimation,” Automatica, vol. 103, pp. 151–158, 2019..

    Article  MathSciNet  MATH  Google Scholar 

  40. Q. Liu, Z. Wang, X. He, and D. H. Zhou, “Event-based distributed filtering with stochastic measurement fading,” IEEE Transactions on Industrial Informatics, vol. 11, no. 6, pp. 1643–1652, 2015.

    Article  Google Scholar 

  41. D. Ding, Z. Wang, and Q.-L. Han, “A set-membership approach to event-triggered filtering for general nonlinear dystems over sensor networks,” IEEE Transactions on Automatic Control, 2019. DOI: https://doi.org/10.1109/TAC.2019.2934389

  42. Q. Liu, Z. Wang, X. He, and D. H. Zhou, “Event-based distributed filtering over Markovian switching topologies,” IEEE Transactions on Automatic Control, vol. 64, no. 4, pp. 1595–1602, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  43. B. Shen, Z. Wang, D. Wang, J. Luo, H. Pu, and Y. Peng, “Finite-horizon filtering for a class of nonlinear time-delayed systems with an energy harvesting sensor,” Automatica, vol. 100, pp. 144–152, 2019..

    Article  MathSciNet  MATH  Google Scholar 

  44. S. Liu, Z. Wang, Y. Chen, and G. Wei, “Protocol-based unscented Kalman filtering in the presence of stochastic uncertainties,” IEEE Transactions on Automatic Control, 2019. DOI: https://doi.org/10.1109/TAC.2019.2929817

    Article  Google Scholar 

  45. L. Wang, Z. Wang, G. Wei, and F. E. Alsaadi, “Observer-based consensus control for discrete-time multiagent systems with coding-decoding communication protocol,” IEEE Transactions on Cybernetics, vol. 49, no. 12, pp. 4335–4345, 2019.

    Article  Google Scholar 

  46. L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation for networked time-delay systems under Round-Robin protocol,” IEEE Transactions on Automatic Control, vol. 64, no. 12, pp. 5191–5198, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  47. L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation of networked nonlinear systems with random access protocol,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2918002

  48. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Transactions on Automatic Control, vol. AC-20, no. 1, pp. 1–10, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  49. S. Attasi, “Systèmes lineaires homogènes à deux indices,” IRIA Rapport Laboria, vol. C-21, no. 31, 1973.

  50. L. Wu, X. Su, and P. Shi, “Mixed H2/H∞ approach to fault detection of discrete linear repetitive processes,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 393–414, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  51. P. M. Sammons, M. L. Gegel, D. A. Bristow, and R. G. Landers, “Repetitive process control of additive manufacturing with application to laser metal deposition,” IEEE Transactions on Control Systems Technology, vol. 27, no. 2, pp. 566–575, 2019.

    Article  Google Scholar 

  52. D. Meng, Y. Jia, J. Du, and S. Yuan, “Robust discrete-time iterative learning control for nonlinear systems with varying initial state shifts,” IEEE Transactions on Automatic Control, vol. 54, no. 11, pp. 2626–2631, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  53. E. Rafajlowicz and W. Rafajlowicz, “Iterative learning in optimal control of linear dynamic processes,” International Journal of Control, vol. 91, no. 7, pp. 1522–1540, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  54. R. Paquin and E. Dubois, “A spatio-temporal gradient method for estimating the displacement field in time-varying imagery,” Computer Vision, Graphics, and Image Processing, vol. 21, no. 2, pp. 205–221, 1983.

    Article  Google Scholar 

  55. D. Zhao, Y. Wang, Y. Li, and S. X. Ding, “H∞ fault estimation for 2-D linear discrete time-varying systems based on Krein space method,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2070–2079, 2018.

    Article  Google Scholar 

  56. Z. Duan, Z. Xiang, and H. R. Karimi, “Stability and l1-gain analysis for positive 2D T-S fuzzy state-delayed systems in the second FM model,” Neurocomputing, vol. 142, pp. 209–215, 2014..

    Article  Google Scholar 

  57. H. R. Shaker and F. Shaker, “Lyapunov stability for continuous-time multidimensional nonlinear systems,” Nonlinear Dynamics, vol. 75, no. 4, pp. 717–724, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  58. N. Yeganefar, N. Yeganefar, M. Ghamgui, and E. Moulay, “Lyapunov theory for 2-D nonlinear Roesser models: application to asymptotic and exponential stability,” IEEE Transactions on Automatic Control, vol. 58, no. 5, pp. 1299–1304, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  59. T. W. S. Chow and Y. Fang, “Two-dimensional learning strategy for multilayer feedforward neural network,” Neurocomputing, vol. 34, nos. 1–4, pp. 195–206, 2000.

    Article  MATH  Google Scholar 

  60. Z. Levnajić and B. Tadić, “Stability and chaos in coupled two-dimensional maps on gene regulatory network of bacterium E-coli,” Chaos, vol. 20, no. 3, pp. 033115, 2010.

    Article  Google Scholar 

  61. J. Liang, Z. Wang, X. Liu, and P. Louvieris, “Robust synchronization for 2-D discrete-time coupled dynamical networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 6, pp. 942–953, 2012.

    Article  Google Scholar 

  62. J. Liang, Z. Wang, Y. Liu, and X. Liu, “State estimation for two-dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays,” International Journal of Robust and Nonlinear Control, vol. 24, no. 1, pp. 18–38, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  63. J. W. Woods and C. H. Radewan, “Kalman filtering in two dimensions,” IEEE Transactions on Information Theory, vol. IT-23, no. 4, pp. 473–482, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  64. J. W. Woods and V. K. Ingle, “Kalman filtering in two dimensions: further results,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-29, no. 2, pp. 188–197, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  65. T. Katayama and M. Kosaka, “Recursive filtering algorithm for a two-dimensional system,” IEEE Transactions on Automatic Control, vol. 24, no. 1, pp. 130–132, 1979.

    Article  MATH  Google Scholar 

  66. A. Concetti and L. Jetto, “Two-dimensional recursive filtering algorithm with edge preserving properties and reduced numerical complexity,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 44, no. 7, pp. 587–591, 1997.

    Article  MATH  Google Scholar 

  67. J. Liang, F. Wang, Z. Wang, and X. Liu, “Minimum-variance recursive filtering for two-dimensional systems with degraded measurements: boundedness and monotonicity,” IEEE Transactions on Automatic Control, vol. 64, no. 10, pp. 4153–4166, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  68. L. H. Keel and S. P. Bhattacharyya, “Robust, fragile, or optimal?” IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1098–1105, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  69. L. Xie, Y. C. Soh, and C. E. de Souza, “Robust Kalman filtering for uncertain discrete-time systems,” IEEE Transactions on Automatic Control, vol. 39, no. 6, pp. 1310–1314, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  70. M. Fu, C. E. de Souza, and Z. Q. Luo, “Finite-horizon robust Kalman filter design,” IEEE Transactions on Signal Processing, vol. 49, no. 9, pp. 2103–2112, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  71. F. Yang, Z. Wang, and Y. S. Hung, “Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1179–1183, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  72. Z. Cao, R. Zhang, Y. Yang, J. Lu, and F. Gao, “Discrete-time robust iterative learning Kalman filtering for repetitive processes,” IEEE Transactions on Automatic Control, vol. 61, no. 1, pp. 270–275, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  73. J. Liang, F. Wang, Z. Wang, and X. Liu, “Robust Kalman filtering for two-dimensional systems with multiplicative noises and measurement degradations: the finite-horizon case,” Automatica, vol. 96, pp. 166–177, 2018..

    Article  MathSciNet  MATH  Google Scholar 

  74. F. Wang, Z. Wang, J. Liang, and X. Liu, “Robust finite-horizon filtering for 2-D systems with randomly varying sensor delays,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 1, pp. 220–232, 2020.

    Article  Google Scholar 

  75. D. Zhao, S. X. Ding, H. R. Karimi, Y. Li, and Y. Wang, “On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: a least squares method,” Automatica, vol. 99, pp. 203–212, 2019..

    Article  MathSciNet  MATH  Google Scholar 

  76. K. Reif, S. Günther, E. Yaz, and R. Unbehauen, “Stochastic stability of the discrete-time extended Kalman filter,” IEEE Transactions on Automatic Control, vol. 44, no. 4, pp. 714–728, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  77. F. Wang, J. Liang, Z. Wang, and X. Liu, “A variance-constrained approach to recursive filtering for nonlinear two-dimensional systems with measurement degradations,” IEEE Transactions on Cybernetics, vol. 48, no. 6, pp. 1877–1887, 2018.

    Article  Google Scholar 

  78. T. Hinamoto, “2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 40, no. 2, pp. 102–110, 1993.

    Article  MATH  Google Scholar 

  79. W.-S. Lu, “On a Lyapunov approach to stability analysis of 2-D digital filters,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 41, no. 10, pp. 665–669, 1994.

    Article  Google Scholar 

  80. C. Du, L. Xie, and Y. C. Soh, “H∞ filtering of 2-D discrete systems,” IEEE Transactions on Signal Processing, vol. 48, no. 6, pp. 1760–1768, 2000.

    Article  MATH  Google Scholar 

  81. L. Xie, C. Du, C. Zhang, and Y. C. Soh, “H∞ deconvolution filtering of 2-D digital systems,” IEEE Transactions on Signal Processing, vol. 50, no. 9, pp. 2319–2332, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  82. H. D. Tuan, P. Apkarian, T. Q. Nguyen, and T. Narikiyo, “Robust mixed H2/H∞ filtering of 2-D systems,” IEEE Transactions on Signal Processing, vol. 50, no. 7, pp. 1759–1771, 2002.

    Article  Google Scholar 

  83. C. E. de Souza, L. Xie, and D. F. Coutinho, “Robust filtering for discrete-time linear systems with convex-bounded parameter uncertainty,” Automatica, vol. 46, no. 4, pp. 673–681, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  84. G. Wei, Z. Wang, W. Li, and L. Ma, “A survey on gain-scheduled control and filtering for parameter-varying systems,” Discrete Dynamics in Nature and Society, vol. 2014, art. no. 105815, 2014.

  85. L. Wu, P. Shi, H. Gao, and C. Wang, “H∞ filtering for 2D Markovian jump systems,” Automatica, vol. 44, no. 7, pp. 1849–1858, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  86. Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information,” Information Sciences, vol. 269, pp. 316–331, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  87. D. Liu, “Lyapunov stability of two-dimensional digital filters with overflow nonlinearities,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 45, no. 5, pp. 574–577, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  88. Y. Luo, Z. Wang, G. Wei, and F. E. Alsaadi, “Robust H∞ filtering for a class of two-dimensional uncertain fuzzy systems with randomly occurring mixed delays,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 1, pp. 70–83, 2017.

    Article  Google Scholar 

  89. B. Boukili, A. Hmamed, A. Benzaouia, and A. El Hajjaji, “H∞ filtering of two-dimensional T-S fuzzy systems,” Circuits, Systems, and Signal Processing, vol. 33, no. 6, pp. 1737–1761, 2014.

    Article  MathSciNet  Google Scholar 

  90. L. Li, W. Wang, and X. Li, “New approach to H∞ filtering of two-dimensional T-S fuzzy systems,” International Journal of Robust and Nonlinear Control, vol. 23, no. 17, pp. 1990–2012, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  91. M. A. Rotea, “The generalized H2 control problem,” Automatica, vol. 29, no. 2, pp. 373–385, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  92. R. M. Palhares and P. L. D. Peres, “Robust filtering with guaranteed energy-to-peak performance-an LMI approach,” Automatica, vol. 36, no. 6, pp. 851–858, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  93. H. Gao and C. Wang, “Robust L2-L∞ filtering for uncertain systems with multiple time-varying state delays,” IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 50, no. 4, pp. 594–599, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  94. L. Wu, Z. Wang, H. Gao, and C. Wang, “H∞ and l2-l∞ filtering for two-dimensional linear parameter-varying systems,” International Journal of Robust and Nonlinear Control, vol. 17, no. 12, pp. 1129–1154, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  95. C. K. Ahn, “l2-l∞ elimination of overflow oscillations in 2-D digital filters described by Roesser model with external interference,” IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 60, no. 6, pp. 361–365, 2013.

    Article  Google Scholar 

  96. Y. Luo, Z. Wang, G. Wei, and F. E. Alsaadi, “Nonfragile l2-l∞ fault estimation for Markovian jump 2-D systems with specified power bounds,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI: https://doi.org/10.1109/TSMC.2018.2794414

  97. C. K. Ahn, P. Shi, and M. V. Basin, “Two-dimensional peak-to-peak filtering for stochastic Fornasini-Marchesini systems,” IEEE Transactions on Automatic Control, vol. 63, no. 5, pp. 1472–1479, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  98. J. C. Willems, “Dissipative dynamical systems part I: general theory,” Archive for Rational Mechanics and Analysis, vol. 45, no. 5, pp. 321–351, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  99. J. C. Willems, “Dissipative dynamical systems part II: linear systems with quadratic supply rates,” Archive for Rational Mechanics and Analysis, vol. 45, no. 5, pp. 352–393, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  100. Z. Feng, J. Lam, and H. Gao, “α-dissipativity analysis of singular time-delay systems,” Automatica, vol. 47, no. 11, pp. 2548–2552, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  101. B. Zhang, W. X. Zheng, and S. Xu, “Filtering of Markovian jump delay systems based on a new performance index,” IEEE Transactions on Circuits and Systems-I: Regular Paper, vol. 60, no. 5, pp. 1250–1263, 2013.

    Article  MathSciNet  Google Scholar 

  102. C. K. Ahn, P. Shi, and H. R. Karimi, “Novel results on generalized dissipativity of two-dimensional digital filters,” IEEE Transactions on Circuits and System-II: Express Briefs, vol. 63, no. 9, pp. 893–897, 2016.

    Article  Google Scholar 

  103. D. Li, J. Liang, and F. Wang, “Dissipative networked filtering for two-dimensional systems with randomly occurring uncertainties and redundant channels,” Neurocomputing, vol. 369, pp. 1–10, 2019.

    Article  Google Scholar 

  104. F. Wang, Z. Wang, J. Liang, and X. Liu, “Resilient state estimation for 2-D time-varying systems with redundant channels: a variance-constrained approach,” IEEE Transactions on Cybernetics, vol. 49, no. 7, pp. 2479–2489, 2019.

    Article  Google Scholar 

  105. Y. Luo, Z. Wang, G. Wei, and F. E. Alsaadi, “H∞ fuzzy fault detection for uncertain 2-D systems under Round-Robin scheduling protocol,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2172–2184, 2017.

    Article  Google Scholar 

  106. F. Wang, Z. Wang, J. Liang, and X. Liu, “Resilient filtering for linear time-varying repetitive processes under uniform quantizations and Round-Robin protocols,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 65, no. 9, pp. 2992–3004, 2018.

    Article  MathSciNet  Google Scholar 

  107. Y. Shen, Z. Wang, B. Shen, F. E. Alsaadi, and F. E. Alsaadi, “Fusion estimation for multi-rate linear repetitive processes under weighted try-once-discard protocol,” Information Fusion, vol. 55, pp. 281–291, 2020.

    Article  Google Scholar 

  108. D. Ding, Z. Wang, and Q.-L. Han, “A scalable algorithm for event-triggered state estimation with unknown parameters and switching topologies over sensor networks,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2917543

  109. L. Ma, Z. Wang, C. Cai, and F. E. Alsaadi, “Dynamic event-triggered state estimation for discrete-time singularly perturbed systems with distributed time-delays,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI: https://doi.org/10.1109/TSMC.2018.2876203

  110. F. Wang, Z. Wang, J. Liang, and X. Liu, “Event-triggered recursive filtering for shift-varying linear repetitive processes,” IEEE Transactions on Cybernetics, 2018. DOI: https://doi.org/10.1109/TCYB.2018.2881312

    Article  Google Scholar 

  111. B. Shen, Z. Wang, D. Wang, and Q. Li, “State-saturated recursive filter design for stochastic time-varying nonlinear complex networks under deception attacks,” IEEE Transactions on Neural Networks and Learning Systems, 2019. DOI: https://doi.org/10.1109/TNNLS.2019.2946290

  112. B. Shen, Z. Wang, D. Wang, and H. Liu, “Distributed state-saturated recursive filtering over sensor networks under Round-Robin protocol,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2932460

  113. Q. Li, B. Shen, Z. Wang, and W. Sheng, “Recursive distributed filtering over sensor networks on Gilbert-Elliott channels: a dynamic event-triggered approach,” Automatica, 2019. DOI: https://doi.org/10.1016/j.automatica.2019.108681

    Article  MathSciNet  Google Scholar 

  114. Q. Li, B. Shen, Z. Wang, T. Huang, and J. Luo, “Synchronization control for a class of discrete time-delay complex dynamical networks: a dynamic event-triggered approach,” IEEE Transactions on Cybernetics, vol. 49, no. 5, pp. 1979–1986, 2019.

    Article  Google Scholar 

  115. Y. Liu, Z. Wang, L. Ma, and F. Alsaadi, “A partial-nodes-based information fusion approach to state estimation for discrete-time delayed stochastic complex networks,” Information Fusion, (ISSN 1566-2535) vol. 49, pp. 240–248, 2019.

    Article  Google Scholar 

  116. Y. Liu, Z. Wang, Y. Yuan, and W. Liu, “Event-triggered partial-nodes-based state estimation for delayed complex networks with bounded distributed delays,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 6, pp. 1088–1098, 2019.

    Article  Google Scholar 

  117. Y. Liu, Z. Wang, Y. Yuan, and F. Alsaadi, “Partial-nodes-based state estimation for complex networks with unbounded distributed delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 8, pp. 3906–3912, 2018.

    Article  MathSciNet  Google Scholar 

  118. Y. Liu, Z. Wang, L. Ma, and F. Alsaadi, “Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays,” Journal of the Franklin Institute, vol. 355, no. 14, pp. 6339–6352, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  119. L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation for networked time-delay systems under Round-Robin protocol,” IEEE Transactions on Automatic Control, vol 64, no. 12, pp. 5191–5198, 2019

    Article  MathSciNet  MATH  Google Scholar 

  120. Y. Yuan, Z. Wang, Y. Yu, L. Guo, and H. Yang, “Active disturbance rejection control for a pneumatic motion platform subject to actuator saturation: an extended state observer approach,” Automatica, vol. 107, pp. 353–361, 2019..

    Article  MathSciNet  MATH  Google Scholar 

  121. M. Wang, Z. Wang, Y. Chen, and W. Sheng, “Event-based adaptive neural tracking control for discrete-time stochastic nonlinear systems: a triggering threshold compensation strategy,” IEEE Transactions on Neural Networks and Learning Systems, 2019. DOI: https://doi.org/10.1109/TNNLS.2019.2927595

  122. D. Ding, Z. Wang, and Q.-L. Han, “Neural-network-based consensus control for multiagent systems with input constraints: the event-triggered case,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2927471

  123. M. Wang, Z. Wang, Y. Chen, and W. Sheng, “Adaptive neural event-triggered control for discrete-time strict-feedback nonlinear systems,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2921733

  124. M. Wang, Z. Wang, Y. Chen, and W. Sheng, “Observer-based fuzzy output-feedback control for discrete-time strict-feedback nonlinear systems with stochastic noises,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2902520

  125. S. Liu, Z. Wang, G. Wei, and M. Li, “Distributed set-membership filtering for multi-rate systems under the Round-Robin scheduling over sensor networks,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2018.2885653

  126. Y. Chen, Z. Wang, Y. Yuan, and P. Date, “Distributed H∞ filtering for switched stochastic delayed systems over sensor networks with fading measurements,” IEEE Transactions on Cybernetics, vol. 50, no. 1, pp. 2–14, 2020.

    Article  Google Scholar 

  127. L. Zou, Z. Wang, Q.-L. Han, and D. H. Zhou, “Full information estimation for time-varying systems with Round-Robin protocol: a recursive filter approach,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2907620

  128. D. Zhao, Z. Wang, D. Ding, and G. Wei, “H∞ PID control with fading measurements: the output-feedback case,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI:10.1109/TSMC.2018.2809489

  129. Z. Zhao, Z. Wang, L. Zou, and G. Guo, “Finite-time state estimation for delayed neural networks with redundant delayed channels,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI: https://doi.org/10.1109/TSMC.2018.2874508

  130. L. Ma, Z. Wang, Y. Liu, and F. E. Alsaadi, “Distributed filtering for nonlinear time-delay systems over sensor networks subject to multiplicative link noises and switching topology,” International Journal of Robust and Nonlinear Control, vol. 29, no. 10, pp. 2941–2959, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  131. L. Zou, Z. Wang, Q.-L. Han, and D. H. Zhou, “Recursive filtering for time-varying systems with random access protocol,” IEEE Transactions on Automatic Control, vol. 64, no. 2, pp. 720–727, 2019.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, P. R. China

    Fan Wang & Jun Yang

  2. Department of Computer Science, Brunel University London, Uxbridge, UB8 3PH, UK

    Zidong Wang

  3. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinling Liang

Authors
  1. Fan Wang
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Correspondence to Jinling Liang.

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Recommended by Editor Jessie (Ju H.) Park. This work was supported in part by the National Natural Science Foundation of China under Grants 61873148, 61973080, 61673110, 61903082 and 61933007, the China Postdoctoral Science Foundation under Grant 2018M640443, and the Jiangsu Planned Projects for Postdoctoral Research Funds of China under Grant 2019K192.

Fan Wang received her B.Sc. degree in mathematics from Hefei Normal University in 2012, and a Ph.D. degree in applied mathematics from Southeast University, Nanjing, China, in 2018. She has published several papers in refereed international journals. Her research interests include stochastic systems, optimal control and robust filtering.

Zidong Wang received his B.Sc. degree in mathematics in 1986 from Suzhou University, Suzhou, China, an M.Sc. degree in applied mathematics in 1990, and a Ph.D. degree in electrical engineering in 1994, both from Nanjing University of Science and Technology, Nanjing, China. He is currently a Professor of Dynamical Systems and Computing in the Department of Computer Science, Brunel University London, U.K. From 1990 to 2002, he held teaching and research appointments in universities in China, Germany and the UK. Prof. Wang’s research interests include dynamical systems, signal processing, bioinformatics, control theory and applications. He has published more than 600 papers in refereed international journals. He is a holder of the Alexander von Humboldt Research Fellowship of Germany, the JSPS Research Fellowship of Japan, William Mong Visiting Research Fellowship of Hong Kong. Prof. Wang serves (or has served) as the Editor-in-Chief for Neurocomputing, the Deputy Editor-in-Chief for International Journal of Systems Science, and an Associate Editor for 12 international journals, including IEEE Transactions on Automatic Control, IEEE Transactions on Control Systems Technology, IEEE Transactions on Neural Networks, IEEE Transactions on Signal Processing, and IEEE Transactions on Systems, Man, and Cybernetics-Part C. He is a Fellow of the IEEE, a Fellow of the Royal Statistical Society and a member of program committee for many international conferences.

Jinling Liang received her B.Sc. and M.Sc. degrees in mathematics from Northwest University, Xi’an, China, in 1997 and 1999, respectively, and a Ph.D. degree in applied mathematics from Southeast University, Nanjing, China, in 2006. She is currently a Professor in the School of Mathematics, Southeast University. She has published around 80 papers in refereed international journals. Her current research interests include stochastic systems, complex networks, robust filtering and bioinformatics. She serves as an associate editor for several international journals.

Jun Yang received his B.Sc. degree from the Department of Automatic Control, Northeastern University, Shenyang, China, in 2006, and a Ph.D. degree in control theory and control engineering from the School of Automation, Southeast University, Nanjing, China, in 2011. He is currently an Associate Professor with the School of Automation, Southeast University. His current research interests include disturbance estimation and compensation, advanced control theory, and its application to flight control systems and motion control systems. Dr. Yang is an Associate Editor of the Transactions of the Instutute of Measurement and Control. He received the Premium Award for best paper of IET Control Theory and Applications in 2017, and the ICI Prize for best paper of Transactions of the Institute of Measurement and Control in 2016.

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Wang, F., Wang, Z., Liang, J. et al. A Survey on Filtering Issues for Two-Dimensional Systems: Advances and Challenges. Int. J. Control Autom. Syst. 18, 629–642 (2020). https://doi.org/10.1007/s12555-019-1000-x

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