×

\(H_\infty\) filtering for piecewise homogeneous Markovian jump nonlinear systems. (English) Zbl 1346.93387

Summary: This paper concerns the problem of \(H_\infty\) filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with \(H_\infty\) performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the \(H_\infty\) filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results.

MSC:

93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
93B36 \(H^\infty\)-control
60J75 Jump processes (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/j.sysconle.2010.11.001 · Zbl 1210.93078 · doi:10.1016/j.sysconle.2010.11.001
[2] DOI: 10.1016/j.automatica.2010.03.007 · Zbl 1192.93119 · doi:10.1016/j.automatica.2010.03.007
[3] Boukas E, Stochastic switching systems analysis and design (2006)
[4] DOI: 10.1109/TSP.2010.2103068 · Zbl 1391.93134 · doi:10.1109/TSP.2010.2103068
[5] DOI: 10.1002/rnc.2909 · Zbl 1284.93231 · doi:10.1002/rnc.2909
[6] DOI: 10.1155/2012/716474 · Zbl 1264.93049 · doi:10.1155/2012/716474
[7] DOI: 10.1109/9.855557 · Zbl 0972.93074 · doi:10.1109/9.855557
[8] DOI: 10.1016/j.sigpro.2012.01.012 · doi:10.1016/j.sigpro.2012.01.012
[9] DOI: 10.1016/j.automatica.2011.08.052 · Zbl 1235.93088 · doi:10.1016/j.automatica.2011.08.052
[10] DOI: 10.1109/TAC.2007.900832 · Zbl 1366.93158 · doi:10.1109/TAC.2007.900832
[11] DOI: 10.1016/j.automatica.2008.03.011 · Zbl 1155.93432 · doi:10.1016/j.automatica.2008.03.011
[12] DOI: 10.1142/p473 · Zbl 1126.60002 · doi:10.1142/p473
[13] DOI: 10.1016/j.jfranklin.2013.08.006 · Zbl 1293.93746 · doi:10.1016/j.jfranklin.2013.08.006
[14] DOI: 10.1109/TAC.2006.883060 · Zbl 1366.93666 · doi:10.1109/TAC.2006.883060
[15] DOI: 10.1016/j.amc.2015.05.061 · doi:10.1016/j.amc.2015.05.061
[16] DOI: 10.1109/TSP.2006.874370 · Zbl 1373.94729 · doi:10.1109/TSP.2006.874370
[17] DOI: 10.1016/j.nonrwa.2012.02.009 · Zbl 1260.60172 · doi:10.1016/j.nonrwa.2012.02.009
[18] DOI: 10.1016/j.eswa.2011.11.111 · doi:10.1016/j.eswa.2011.11.111
[19] Xu S., Robust control and filtering of singular systems (2006) · Zbl 1114.93005
[20] DOI: 10.1080/00207720903513350 · Zbl 1231.93114 · doi:10.1080/00207720903513350
[21] DOI: 10.1016/j.sigpro.2013.03.003 · doi:10.1016/j.sigpro.2013.03.003
[22] Yu X., IEEE Transactions on Automatic Control 2 pp 304– (2010) · Zbl 1368.93584 · doi:10.1109/TAC.2009.2034924
[23] DOI: 10.1109/TCSI.2013.2246213 · doi:10.1109/TCSI.2013.2246213
[24] DOI: 10.1016/j.automatica.2009.07.004 · Zbl 1180.93100 · doi:10.1016/j.automatica.2009.07.004
[25] DOI: 10.1016/j.apm.2013.11.050 · doi:10.1016/j.apm.2013.11.050
[26] DOI: 10.1007/s12555-012-9114-4 · doi:10.1007/s12555-012-9114-4
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.