Document Type : Review Article
Authors
Abstract
This paper considers the problem of robust H∞ filter design in uncertain discrete-time singular systems with possible missing measurements due to unreliable network transmission channels. The stochastic variable satisfying Bernoulli random binary distribution is introduced to model the missing phenomena and the corresponding filtering error dynamics with delay is then induced. We provide a set of sufficient conditions for the existence of the desired filter, and propose a robust filter design method under a strict linear matrix inequality framework. A numerical example is given to illustrate the effectiveness of the proposed method.
Keywords
[1] S. F. Chen and I-K. Fong, “Robust filtering for 2-d state-delayed systems with NFT uncertainties,” IEEE Trans. Signal Process., vol. 54, pp 274-285, 2006.
[2] L. Dai, Singular Control Systems, Berlin: Springer-Verlag, 1989.
[3] E. Fridman and U. Shaked, “A new H_∞ filter design for linear time delay systems,” IEEE Trans. Signal Process., vol. 49, pp. 2839-2843, 2001.
[4] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox – for Use with MATLAB, The Math Works Inc., Natick, MA, 1995.
[5] C. M. Lee and I-K. Fong, “H_∞ filter design for uncertain discrete-time singular systems via normal transformation,” Circuits Syst. & Signal Process., vol. 25, pp. 525-538, 2006.
[6] C. M. Lee and I-K. Fong, “H_∞ optimal singular and normal filter design for uncertain singular systems,” IET Contr. Theory & Applications, vol. 1, pp. 119-126, 2007.
[7] C. M. Lee and W. S. Wang, “Robust H_∞ filtering for uncertain discrete-time singular systems,” in proc. 2008 IFAC World Congress, pp. 2687-2692.
[8] C. M. Lee and M. H. Hsieh, “Networked filtering for singular systems with unreliable channels, ” in proc. 2010 Int. Conf. on Information Science, Signal Processing and their Applications, pp. 422-425.
[9] R. Lu, H. Su, J. Chu, S. Zhou, and M. Fu, “Reduced-order H_∞ filtering for discrete-time singular systems with lossy measurements,” IET Contr. Theory & Applications, vol. 4, pp. 151-163, 2010.
[10] Z. Q. Luo, J. F. Sturm, and S. Zhang, “Multivariate nonnegative quadratic mappings,” SIAM J. Optim., vol. 14, pp. 1140-1162, 2004.
[11] A. W. Pila, U. Shaked, and C. E. De Souza, “H_∞ filtering for continuous-time linear systems with delay,” IEEE Trans. Automat. Contr., vol. 44, pp. 1412-1417, 1999.
[12] C. E. De Souza, R. M. Palhares, and P. L. D. Peres, “Robust H_∞ filter design for uncertain linear systems with multiple time-varying state delays,” IEEE Trans. Signal Process., vol. 49, pp. 569-576, 2001.
[13] S. Sun, L. Xie, W. Xiao, and Nan Xiao, “Optimal filtering for systems with multiple packet dropouts,” IEEE Trans. Circuits Syst. II, vol. 55, pp. 695-699, 2008.
[14] Z. Wang, F. Yang, W. C. Ho, and X. Liu, “Robust H_∞ filtering for stochastic time-delay systems with missing measurements,” IEEE Trans. Signal Process., vol. 54, pp. 2579-2587, 2006.
[15] S. Y. Xu and T. Chen, “Reduced-order H_∞ filtering for stochastic systems,” IEEE Trans. Signal Process., vol. 50, pp. 2998-3007, 2002.
[16] S. Xu, J. Lam, and L. Zhang, “Robust D-stability analysis for uncertain discrete singular systems with state delay,” IEEE Trans. Circuits and Systems - I, vol. 49, pp. 551-555, 2002.
[17] S. Y. Xu and J. Lam, “Reduced-order H_∞ filtering for singular systems,” Systems & Contr. Lett., vol. 56, pp. 48-57, 2007.
[18] F. W. Yang, Z. Wang, Y. S. Hung and M. Gani, “H_∞ control for networked systems with random communication delays,” IEEE Trans. Automat. Contr., vol. 51, pp. 511-518, 2006.
H. Zhang, D. Zhang, and L. Xie, “An innovation approach to H_∞ prediction with application to systems with delayed measurements,” Automatica, vol. 40, pp. 1253-1261, 2004.
)