# 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.

## Keywords

Singular Markovian jump systems Filtering Intermittent measurements Time-varying delay## Notes

### 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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