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Filtering for a class of nonlinear discrete-time stochastic systems with state delays. (English) Zbl 1152.93053
For a class of nonlinear discrete time stochastic systems with state delays, the filtering problem is investigated. The researchers developed an algebraic matrix inequality approach to deal with the filter analysis problem, then, they derived a sufficient condition for the existence of the desired filters. The filter design problem is tackled based on the generalized inverse theory. An empirical example is provided to demonstrate the importance of the proposed design method.

93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
93E03 Stochastic systems in control theory (general)
15A45 Miscellaneous inequalities involving matrices
15A29 Inverse problems in linear algebra
Full Text: DOI
[1] Ben-Israel, A.; Greville, T.N.E., Generalized inverses: theory and applications, (1974), Wiley New York · Zbl 0305.15001
[2] E. Beran, K. Grigoriadis, A combined alternating projections and semidefinite programming algorithm for low-order control design, in: Preprints of 13th IFAC World Congress, vol. C, San Francisco, CA, USA, 1996, pp. 85-90.
[3] Boukas, E.K.; Liu, Z.-K., Deterministic and stochastic time-delay systems, (2002), Birkhauser Boston · Zbl 0998.93041
[4] Elanayar, V.T.S.; Shin, Y.C., Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems, IEEE trans. neural networks, 5, 594-603, (1994)
[5] Fleming, W.H.; McEneaney, W.M., A MAX-plus-based algorithm for a hamilton – jacobi – bellman equation of nonlinear filtering, SIAM J. control optim., 38, 683-710, (2000) · Zbl 0949.35039
[6] Fridman, E.; Shaked, U.; Xie, L., Robust \(H_2\) filtering of linear systems with time delays, Int. J. robust & nonlinear control, 13, 983-1010, (2003)
[7] Gelb, A., Applied optimal estimation, (1974), Cambridge University Press Cambridge
[8] J.C. Geromel, P.L.D. Peres, S.R. Souza, Output feedback stabilization of uncertain systems through a min/max problem, in: Preprints of 12th IFAC World Congress, vol. 6, Sydney, Australia, 1993, pp. 35-38.
[9] Glover, K., All optimal Hankel-norm approximations of linear multivariable systems and their \(L^\infty\)-error bounds, Int. J. control, 39, 1115-1193, (1984) · Zbl 0543.93036
[10] Nguang, S.K.; Shi, P., Nonlinear \(H_\infty\) filtering of sampled-data systems, Automatica, 36, 303-310, (2000) · Zbl 0943.93041
[11] Nguang, S.K.; Shi, P., \(H_\infty\) filtering design for uncertain nonlinear systems under sampled measurements, Int. J. systems sci., 32, 889-898, (2001) · Zbl 1010.93102
[12] Saberi, A.; Sannuti, P.; Chen, B.M., \(H_2\) optimal control, (1995), Prentice Hall International London
[13] Tarn, T.-J.; Rasis, Y., Observers for nonlinear stochastic systems, IEEE trans. automat. control, 21, 441-448, (1976) · Zbl 0332.93075
[14] Wang, Z.; Burnham, K.J., Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation, IEEE trans. signal process., 49, 794-804, (2001)
[15] Wang, Z.; Ho, D.W.C., Filtering on nonlinear time-delay stochastic systems, Automatica, 39, 101-109, (2003) · Zbl 1010.93099
[16] Wang, Z.; Lam, J.; Liu, X., Nonlinear filtering for state delayed systems with Markovian switching, IEEE trans. signal process., 51, 2321-2328, (2003) · Zbl 1369.94314
[17] Xie, L.; Soh, Y.C.; de Souza, C.E., Robust Kalman filtering for uncertain discrete-time systems, IEEE trans. automat. control, 39, 1310-1314, (1994) · Zbl 0812.93069
[18] S. Xu, J. Lam, Robust output feedback stabilization of uncertain discrete time-delay stochastic systems with multiplicative noise, Dynamics Continuous Discrete Impulsive Systems 12 (2005) 41-58. · Zbl 1105.93060
[19] Yuan, C.; Mao, X., Robust stability and controllability of stochastic differential delay equations with Markovian switching, Automatica, 40, 3, 343-354, (2004) · Zbl 1040.93069
[20] Zhu, X.; Soh, Y.C.; Xie, L., Robust Kalman filters design for discrete time-delay systems, Circuits systems signal process., 21, 3, 319-335, (2002) · Zbl 1022.93047
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