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Extended Robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Filter Design for Discrete Time-Invariant Linear Systems with Polytopic Uncertainty

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Abstract

This paper is concerned with the problem of robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) filter design for discrete-time linear time-invariant systems with polytopic parameter uncertainties. Less conservative robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) filter design procedures are proposed in terms of single-parameter minimization problems with linear matrix inequality constraints. To this end, we generalize the filter structures available in the literature to date in such a way that the filter’s next state is built by summing the filter’s states over several samples from the past to the present. For stability of the filtering error system, the homogeneous polynomial parameter-dependent Lyapunov functions are employed. Finally, illustrative examples are given to demonstrate the merits of the proposed methods.

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Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for their careful reading and constructive suggestions. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2012R1A2A2A01014088) and the Human Resources Development program (No. 20124010203240) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Yonsei University, Seodaemun-gu, Seoul, 120-749, Korea

    Dong Hwan Lee

  2. Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea

    Young Hoon Joo

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  1. Dong Hwan Lee
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Correspondence to Young Hoon Joo.

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Lee, D.H., Joo, Y.H. Extended Robust \(\mathcal{H}_{2}\) and \(\mathcal{H}_{\infty}\) Filter Design for Discrete Time-Invariant Linear Systems with Polytopic Uncertainty. Circuits Syst Signal Process 33, 393–419 (2014). https://doi.org/10.1007/s00034-013-9658-4

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  • DOI: https://doi.org/10.1007/s00034-013-9658-4

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