Geodesic
Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays
Kybernetika, Tome 50 (2014) no. 4, pp. 491-511.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

This paper is concerned with the exponential $H_{\infty}$ filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and $H_{\infty}$ control problem. Then, a mean-square exponentially stable and Markovian jump filter is designed such that the filtering error system is mean-square exponentially stable and the $H_{\infty}$ performance of estimation error can be ensured. Besides, the derivative of discrete time-varying delay $h(t)$ satisfies $\dot{h}(t)\leq\eta$ and simultaneously the decay rate $\beta$ can be finite positive value without equation constraint. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.
DOI : 10.14736/kyb-2014-4-0491
Classification : 93B36, 93E03
Keywords: stochastic systems; distributed time-varying delay; $H_{\infty }$ filter; linear matrix inequality 
@article{10_14736_kyb_2014_4_0491,
     author = {Ma, Li and Xu, Meimei and Jia, Ruting and Ye, Hui},
     title = {Exponential $H_{\infty }$ filter design for stochastic {Markovian} jump systems with both discrete and distributed time-varying delays},
     journal = {Kybernetika},
     pages = {491--511},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2014},
     doi = {10.14736/kyb-2014-4-0491},
     mrnumber = {3275081},
     zbl = {06386423},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0491/}
}
TY  - JOUR
AU  - Ma, Li
AU  - Xu, Meimei
AU  - Jia, Ruting
AU  - Ye, Hui
TI  - Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays
JO  - Kybernetika
PY  - 2014
SP  - 491
EP  - 511
VL  - 50
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0491/
DO  - 10.14736/kyb-2014-4-0491
LA  - en
ID  - 10_14736_kyb_2014_4_0491
ER  - 
%0 Journal Article
%A Ma, Li
%A Xu, Meimei
%A Jia, Ruting
%A Ye, Hui
%T Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays
%J Kybernetika
%D 2014
%P 491-511
%V 50
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0491/
%R 10.14736/kyb-2014-4-0491
%G en
%F 10_14736_kyb_2014_4_0491
Ma, Li; Xu, Meimei; Jia, Ruting; Ye, Hui. Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays. Kybernetika, Tome 50 (2014) no. 4, pp. 491-511. doi : 10.14736/kyb-2014-4-0491. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-4-0491/

Cité par Sources :