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Hankel-type model reduction for linear repetitive processes: differential and discrete cases

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Abstract

This paper investigates a Hankel-type model reduction problem for linear repetitive processes. Both differential and discrete cases are considered. For a given stable along the pass process, our attention is focused on the construction of a reduced-order stable along the pass process, which guarantees the corresponding error process to have a specified Hankel-type error performance. The Hankel-type performances are first established for differential and discrete linear repetitive processes, respectively, and the corresponding model reduction problems are solved by using the projection approach. Since these obtained conditions are not expressed in linear matrix inequality (LMI) form, the cone complementary linearization (CCL) method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be solved efficiently. Three numerical examples are provided to demonstrate the proposed theory.

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Authors and Affiliations

  1. College of Automation Science and Engineering, South China University of Technology, Wushan Road, Tianhe District, Guangzhou, China

    Ligang Wu

  2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    James Lam

Authors
  1. Ligang Wu
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  2. James Lam
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Correspondence to James Lam.

Additional information

This work was partially supported by RGC HKU 7028/04P.

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Wu, L., Lam, J. Hankel-type model reduction for linear repetitive processes: differential and discrete cases. Multidim Syst Sign Process 19, 41–78 (2008). https://doi.org/10.1007/s11045-007-0031-2

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  • DOI: https://doi.org/10.1007/s11045-007-0031-2

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