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Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay

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Abstract

This paper presents central finite-dimensional H ∞ filters for linear systems with state or measurement delay that are suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including an attenuation control term with opposite sign. In contrast to the results previously obtained for linear time-delay systems, the paper reduces the original H ∞ filtering problems to H 2 (optimal mean-square) filtering problems, using the technique proposed in Doyle et al. (IEEE Trans. Automat. Contr. AC-34:831–847, 1989). The paper first presents a central suboptimal H ∞ filter for linear systems with state delay, based on the optimal H 2 filter from Basin et al. (IEEE Trans. Automat. Contr. AC-50:684–690, 2005), which contains a finite number of filtering equations for any fixed filtering horizon, but this number grows unboundedly as time goes to infinity. To overcome that difficulty, an alternative central suboptimal H ∞ filter is designed for linear systems with state delay, which is based on the alternative optimal H 2 filter from Basin et al. (Int. J. Adapt. Control Signal Process. 20(10):509–517, 2006). Then, the paper presents a central suboptimal H ∞ filter for linear systems with measurement delay, based on the optimal H 2 filter from Basin and Martinez-Zuniga (Int. J. Robust Nonlinear Control 14(8):685–696, 2004). Numerical simulations are conducted to verify the performance of the designed three central suboptimal filters for linear systems with state or measurement delay against the central suboptimal H ∞ filter available for linear systems without delays.

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Authors and Affiliations

  1. Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon, Apdo postal 144-F, C.P. 66450, San Nicolas de los Garza, Nuevo Leon, Mexico

    Michael Basin & Dario Calderon-Alvarez

  2. Department of Computing and Mathematical Sciences, Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kingdom

    Peng Shi

  3. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jianfei Wang

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  1. Michael Basin
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  2. Peng Shi
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  3. Dario Calderon-Alvarez
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  4. Jianfei Wang
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Correspondence to Michael Basin.

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The authors thank The London Royal Society (RS) and the Mexican National Science and Technology Council (CONACyT) for financial support under an RS International Incoming Short Visits 2006/R4 Grant and CONACyT Grants 55584 and 52953.

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Basin, M., Shi, P., Calderon-Alvarez, D. et al. Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay. Circuits Syst Signal Process 28, 305–330 (2009). https://doi.org/10.1007/s00034-008-9077-0

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  • DOI: https://doi.org/10.1007/s00034-008-9077-0

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