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\(\mathcal {H}_{\infty }\) filtering for sample data systems with stochastic sampling and Markovian jumping parameters

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Abstract

This paper deals with the problem of \(\mathcal {H}_{\infty }\) filtering for sample data systems that possess random jumping parameters described by a finite-state Markov process with stochastic sampling. Multiple stochastic sampling periods are considered in which each sampling period is assumed to be time varying that switches between two different values in a random way with given probability. The aim of this paper is to design a filter such that the filtering error system is stochastically stable with a prescribed \(\mathcal {H}_{\infty }\) disturbance attenuation level. Sufficient conditions for the existence of \(\mathcal {H}_{\infty }\) filters are expressed in terms of linear matrix inequalities (LMIs), which can be solved by using Matlab LMI toolbox. Numerical examples are given to illustrate the effectiveness of the proposed result including a realistic Transmission Control Protocol network model.

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Acknowledgments

The work of V. M. Revathi was supported by UGC-BSR-Research fellowship in Mathematical Sciences-2012-13, Govt. of India, New Delhi. The work of J.H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2013R1A1A2A10005201).

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram , 624 302, Tamil Nadu, India

    V. M. Revathi & P. Balasubramaniam

  2. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan , 712-749, Republic of Korea

    Ju H. Park & Tae H. Lee

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  1. V. M. Revathi
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  2. P. Balasubramaniam
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  3. Ju H. Park
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  4. Tae H. Lee
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Correspondence to P. Balasubramaniam or Ju H. Park.

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Revathi, V.M., Balasubramaniam, P., Park, J.H. et al. \(\mathcal {H}_{\infty }\) filtering for sample data systems with stochastic sampling and Markovian jumping parameters. Nonlinear Dyn 78, 813–830 (2014). https://doi.org/10.1007/s11071-014-1479-x

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  • DOI: https://doi.org/10.1007/s11071-014-1479-x

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