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(Generalized) KYP lemma and applications

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Encyclopedia of Systems and Control

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Abstract

Various properties of dynamical systems can be characterized in terms of inequality conditions on their frequency responses. The Kalman-Yakubovich-Popov (KYP) lemma shows equivalence of such frequency domain inequality (FDI) and a linear matrix inequality (LMI). The fundamental result has been a basis for robust and optimal control theories in the past several decades. The KYP lemma has recently been generalized to the case where an FDI on a possibly improper transfer function is required to hold in a (semi)finite frequency range. The generalized KYP lemma allows us to directly deal with practical situations where design parameters are sought to satisfy FDIs in multiple (semi)finite frequency ranges. Various design problems, including FIR filter and PID controller, reduce to LMI problems which can be solved via semidefinite programming.

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Authors and Affiliations

  1. Department of Mechanical & Aerospace Engineering, University of California, 420 Westwood Plaza, 90095, Los Angeles, CA, USA

    Ph.D Tetsuya Iwasaki

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  1. Ph.D Tetsuya Iwasaki
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Correspondence to Tetsuya Iwasaki .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Iwasaki, T. (2013). (Generalized) KYP lemma and applications. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_160-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_160-1

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  • Online ISBN: 978-1-4471-5102-9

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