Exponential H ∞ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays

Li Ma; Meimei Xu; Ruting Jia; Hui Ye

Kybernetika (2014)

  • Volume: 50, Issue: 4, page 491-511
  • ISSN: 0023-5954

Abstract

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This paper is concerned with the exponential H ∞ 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 ∞ 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 ∞ performance of estimation error can be ensured. Besides, the derivative of discrete time-varying delay h ( t ) satisfies h ˙ ( t ) ≤ η and simultaneously the decay rate β can be finite positive value without equation constraint. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.

How to cite

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Ma, Li, et al. "Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays." Kybernetika 50.4 (2014): 491-511. <http://eudml.org/doc/262043>.

@article{Ma2014,
abstract = {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)\le \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.},
author = {Ma, Li, Xu, Meimei, Jia, Ruting, Ye, Hui},
journal = {Kybernetika},
keywords = {stochastic systems; distributed time-varying delay; $H_\{\infty \}$ filter; linear matrix inequality; stochastic systems; distributed time-varying delay; filter; linear matrix inequality},
language = {eng},
number = {4},
pages = {491-511},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exponential $H_\{\infty \}$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays},
url = {http://eudml.org/doc/262043},
volume = {50},
year = {2014},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 4
SP - 491
EP - 511
AB - 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)\le \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.
LA - eng
KW - stochastic systems; distributed time-varying delay; $H_{\infty }$ filter; linear matrix inequality; stochastic systems; distributed time-varying delay; filter; linear matrix inequality
UR - http://eudml.org/doc/262043
ER -

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Citations in EuDML Documents

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  1. Hui Li, Ming Lyu, Baozhu Du, Event-based multi-objective filtering for multi-rate time-varying systems with random sensor saturation
  2. Lili Xu, Sunjie Zhang, Licheng Wang, Distributed resilient filtering of large-scale systems with channel scheduling
  3. Altuğ İftar, Extension principle and controller design for systems with distributed time-delay
  4. Lingchun Li, Guangming Zhang, Meiying Ou, Yujie Wang, H ∞ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities

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