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Quantized Finite-Time Non-fragile Filtering for Singular Markovian Jump Systems with Intermittent Measurements

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Abstract

In this work, the finite-time non-fragile mixed \(H_\infty \) and passivity filter design problem for a class of discrete-time singular Markovian jump systems with time-varying delays, intermittent measurements and quantization is investigated. The measured output of the plant is quantized by a logarithmic mode-independent quantizer, and the time-varying transition probability matrix is described by a polytope. In this work, it is considered that the missing measurement phenomenon occurs during signal transmission from the plant to the filter, which is described by a stochastic variable that obeys the Bernoulli random binary distribution. Then, by constructing a proper Lyapunov–Krasovskii functional and using the linear matrix inequality (LMI) technique, sufficient conditions are obtained, which ensures that the augmented filtering system is stochastically finite-time boundedness with a prescribed mixed \(H_\infty \) and passive performance index. Moreover, the filter gains can be computed in terms of solution to a set of LMIs. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed filter design technique.

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Acknowledgements

The work of M. Sathishkumar was supported by the RGNF, UGC, New Delhi, India [Grant no. F1-17.1/2015-16/RGNF-2015-17-SC-TAM-18857/(SA-III/Website), dated: 09-01-2016].

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Authors and Affiliations

  1. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    Sakthivel Rathinasamy

  2. Department of Mathematics, Anna University Regional Campus, Coimbatore, 641046, India

    Sathishkumar Murugesan

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Faris Alzahrani

  4. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Yong Ren

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  1. Sakthivel Rathinasamy
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  2. Sathishkumar Murugesan
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  3. Faris Alzahrani
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  4. Yong Ren
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Correspondence to Sakthivel Rathinasamy.

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Rathinasamy, S., Murugesan, S., Alzahrani, F. et al. Quantized Finite-Time Non-fragile Filtering for Singular Markovian Jump Systems with Intermittent Measurements. Circuits Syst Signal Process 38, 3971–3995 (2019). https://doi.org/10.1007/s00034-019-01046-9

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