\(l_2-l_\infty\) filtering for multirate systems based on lifted models. (English) Zbl 1173.93360

Summary: For a multirate sample-data system where the output sampling rate is slower than the input updating rate, we study the \(l_2-l_\infty\) filtering problems for fast state estimation by using the lifted model. The filtering problem is handled in the framework of linear matrix inequalities with a nonconvex constraint, which is numerically solved by the product reduction algorithm. Finally, the effectiveness of the proposed method is illustrated and verified by simulation examples.


93C57 Sampled-data control/observation systems
93C35 Multivariable systems, multidimensional control systems
93C55 Discrete-time control/observation systems
Full Text: DOI


[1] S.P. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994) · Zbl 0816.93004
[2] T. Chen, B. Francis, Optimal Sampled-Data Control Systems (Springer, London, 1995) · Zbl 0847.93040
[3] M.C. de Oliveira, J.C. Geromel, Numerical comparison of output feedback design methods, in Proc. of American Control Conference, vol. 1, pp. 72–76, 1997
[4] C.E. de Souza, R.M. Palhares, P.L.D. Peres, Robust H filter design for uncertain linear systems with multiple time-varying state delays. IEEE Trans. Signal Process. 49, 569–576 (2001) · Zbl 1369.93667
[5] D. Farret, G. Duc, J.R. Harcaut, Multirate LPV synthesis: a loop-shaping approach for missile control, in Proc. of American Control Conference, vol. 5. pp. 4092–4097 (2002)
[6] H. Gao, C. Wang, Robust energy-to-peak filtering with improved LMI representations. IEE Proc. Vis. Image Signal Process. 150, 82–89 (2003)
[7] J.C. Geromel, M.C. de Oliveira, H 2 and H robust filtering for convex bounded uncertain systems. IEEE Trans. Autom. Control 46, 100–107 (2001) · Zbl 1056.93628
[8] J.C. Geromel, J. Bernussou, G. Garcia, M.C. De Oliveira, H 2 and H robust filtering for discrete-time linear systems. SIAM J. Control Optim. 38, 1353–1368 (2000) · Zbl 0958.93091
[9] K.M. Grigoriadis, J.T. Watson, Reduced order H and L 2 filtering via linear matrix inequalities. IEEE Trans. Aerosp. Electron. Syst. 33(4), 1326–1338 (1997)
[10] R.D. Gudi, S.L. Shah, M.R. Gray, Adaptive multirate state and parameter estimation strategies with application to a bioreactor. AIChE J. 41, 2451–2464 (1995)
[11] M. Nemani, T.C. Tsao, S. Hutchinson, Multi-rate analysis and design of visual feedback digital servo-control system. J. Dyn. Syst. Meas. Control 116, 45–55 (1994) · Zbl 0800.93397
[12] P.G. Park, T. Kailath, H filtering via convex optimization. Int. J. Control 66, 15–22 (1997) · Zbl 0870.93041
[13] J. Sheng, Optimal filtering for multirate systems based on lifted models, in Proc. of American Control Conference, vol. 5, pp. 3459–3461 (2005)
[14] J. Sheng, T. Chen, S.L. Shah, Optimal filtering for multirate systems. IEEE Trans. Circuits Syst. II: Express Briefs 52, 228–232 (2005)
[15] Y. Shi, T. Chen, 2-norm based iterative design of filterbank transceivers: a control perspective. J. Control Sci. Eng. Article ID 143085, vol. 2008, doi: 10.1155/2008/143085 · Zbl 1229.94020
[16] Y. Shi, F. Ding, T. Chen, 2-norm based recursive design of transmultiplexers with designable filter length. Circuits Syst. Signal Process. 25, 447–462 (2006) · Zbl 1130.94312
[17] Y. Shi, F. Ding, T. Chen, Multirate crosstalk identification in xDSL systems. IEEE Trans. Commun. 54, 1878–1886 (2006)
[18] G. Siouris, An Engineering Approach to Optimal Control and Estimation Theory (Wiley, New York, 1996)
[19] H. Sorenson, Kalman Filtering: Theory and Applications (IEEE Press, New York, 1985)
[20] J. Xia, S. Xu, B. Song, Delay-dependent L 2 filter design for stochastic time-delay systems. Syst. Control Lett. 56, 579–587 (2007) · Zbl 1157.93530
[21] S. Xu, T. Chen, Reduced-order H filtering for stochastic systems. IEEE Trans. Signal Process. 50, 2998–3007 (2002) · Zbl 1369.94325
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.