DocumentCode :
2385795
Title :
Discrete-time Markovian jump linear systems with partly unknown transition probabilities: H filtering problem
Author :
Zhang, Lixian ; Boukas, El Kebir
Author_Institution :
Mech. Eng. Dept., Ecole Polytech. de Montreal, Montreal, QC
fYear :
2008
fDate :
11-13 June 2008
Firstpage :
2272
Lastpage :
2277
Abstract :
The problem of Hinfin filtering for a class of discrete-time Markovian jump linear systems (MJLS) with partly unknown transition probabilities is investigated in the paper. The considered systems are more general, which cover the MJLS with completely known and completely unknown transition probabilities as two special cases. A mode-dependent full-order filter is constructed and the bounded real lemma (BRL) for the resulting filtering error system is derived via LMI formulation. Then, an improved version of the BRL is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and Lyapunov matrices among different operation modes. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed Hinfin performance index. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.
Keywords :
Hinfin control; Lyapunov matrix equations; Markov processes; discrete time systems; filtering theory; linear systems; stability; stochastic systems; Hinfin filtering problem; Hinfin performance index; LMI formulation; Lyapunov matrices; bounded real lemma; cross coupling elimination; discrete-time Markovian jump linear systems; filtering error system; mode-dependent full-order filter; slack matrix variables; transition probabilities; unknown transition probabilities; Control systems; Difference equations; Differential equations; Filtering; Linear systems; Nonlinear filters; Performance analysis; Robustness; Stochastic processes; Stochastic systems;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference, 2008
Conference_Location :
Seattle, WA
ISSN :
0743-1619
Print_ISBN :
978-1-4244-2078-0
Electronic_ISBN :
0743-1619
Type :
conf
DOI :
10.1109/ACC.2008.4586830
Filename :
4586830
Link To Document :
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