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Quadratic Robust Filter Design

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Robust Filtering for Uncertain Systems

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

This chapter investigates robust filtering problems using the quadratic approach. For each filtering scheme, the optimal filter design methods for nominal systems are derived first by performing some linearization procedures, and then extended to deal with robust filtering problems based on the quadratic stability notion in robust control theory. All the design methods are given in terms of linear matrix inequality (LMI). Three filtering schemes are addressed in this chapter, namely (robust) \(H_{2}\), H-infinity, and energy-to-peak filtering. \(H_{2}\) filters assume Gaussian white noises, and robust \(H_{2}\) filters improve the robustness against parametric uncertainty in systems; H-infinity and energy-to-peak filters assume energy-bounded noises, so that they can deal with both Gaussian and non-Gaussian noises, more robust than \(H_{2}\) filters in dealing with uncertainty in signals. Moreover, the relationship between the LMI approaches to optimal \(H_{2}\) filter design and the Kalman filtering method is revealed. Several numerical examples are provided to illustrate the effectiveness of the filter design methods presented in this chapter.

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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). Quadratic 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-05903-7_2

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  • Online ISBN: 978-3-319-05903-7

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