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Design of Robust Strictly Positive Real Transfer Functions

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Networked Control Systems

Abstract

This chapter studies the robust synthesis problem for strictly positive real (SPR) transfer functions. The concepts of SPR regions and weak SPR regions are introduced. By using the complete discrimination system (CDS) for polynomials, complete characterization of the (weak) SPR regions for transfer functions in coefficient space is given. It is shown that the weak monic SPR region associated with a fixed polynomial is bounded and the intersection of several weak monic SPR regions associated with different polynomials cannot be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low-order and high-order polynomial families. Especially, the derived conditions are necessary and sufficient for robust SPR design of polynomial segment or low-order (n ≤ 4) interval polynomials. Illustrative examples are provided to show the effectiveness of this algorithm.

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Author information

Authors and Affiliations

  1. Institute of Automation, Chinese Academy of Sciences Beijing, 100080, P. R. China

    Wensheng Yu

  2. Peking University, Beijing, 100871, P. R. China

    Long Wang

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  1. Wensheng Yu
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  2. Long Wang
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Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Fei-Yue Wang PhD

  2. Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Derong Liu PhD

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Yu, W., Wang, L. (2008). Design of Robust Strictly Positive Real Transfer Functions. In: Wang, FY., Liu, D. (eds) Networked Control Systems. Springer, London. https://doi.org/10.1007/978-1-84800-215-9_11

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  • DOI: https://doi.org/10.1007/978-1-84800-215-9_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-214-2

  • Online ISBN: 978-1-84800-215-9

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