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Robust Filtering for Uncertain Systems pp 83–121Cite as

Parameter-Dependent Robust Filter Design

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Abstract

This chapter studies parameter-dependent approaches to robust filter design, so as to reduce the conservatism of quadratic approaches presented in Chap. 2. By virtue of the Projection Lemma, dilated conditions are derived, where slack matrices are introduced to eliminate the product terms between Lyapunov matrices and system matrices. Then linearly parameter-dependent approaches and polynomially parameter-dependent approaches to robust filter design are developed respectively, and all the design methods are given in terms of linear matrix inequality. The former is derived by imposing the Lyapunov matrices to be linearly parameter-dependent and fixing the slack matrices to be constant, respectively, while the latter is obtained by rendering the Lyapunov matrices and slack matrices both to be homogeneous polynomials of the certainty parameters with the same degree. Numerical examples clearly show the improvement of parameter-dependent approaches in this chapter over the quadratic approaches in Chap. 2.

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Authors and Affiliations

  1. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China

    Huijun Gao & Xianwei Li

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  1. Huijun Gao
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  2. Xianwei Li
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Correspondence to Huijun Gao .

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Gao, H., Li, X. (2014). Parameter-Dependent Robust Filter Design. In: Robust Filtering for Uncertain Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-05903-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-05903-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05902-0

  • Online ISBN: 978-3-319-05903-7

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