Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays

Yakufu Kasimu; Gulijiamali Maimaitiaili; Yakufu Kasimu; Gulijiamali Maimaitiaili

doi:10.3934/math.2024752

AIMS Mathematics

2024, Volume 9, Issue 6: 15559-15583. doi: 10.3934/math.2024752

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Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays

Yakufu Kasimu ¹,
Gulijiamali Maimaitiaili ^{1,2
,
,}

1.
School of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang 830017, China
2.
Xinjiang Key Laboratory of Mental Development and Learning Science, China

Received: 29 February 2024 Revised: 29 March 2024 Accepted: 24 April 2024 Published: 29 April 2024
MSC : 93C15, 93B36

This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.
- parameter uncertainties,
- Markovian jump systems,
- neutral delay,
- non-fragile H_∞ filter
Citation: Yakufu Kasimu, Gulijiamali Maimaitiaili. Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays[J]. AIMS Mathematics, 2024, 9(6): 15559-15583. doi: 10.3934/math.2024752

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Abstract

This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.

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