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An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems

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Abstract

Combined use of the method of sum of squares (SOS) and quantifier elimination (QE) is discussed with regard to the problem of nonlinear gain analysis for a class of dynamical systems. SOS, a numerical method, is used to search for the structure of a gain function quickly, and QE, a symbolic method, determines all gain functions in the structure to find the minimum gain function. QE can also be used for the infeasibility check of gain structures. A proposed analysis procedure for polynomial dynamical systems prevents unnecessary searching for a gain structure. Two illustrative examples show the effectiveness of the proposed gain analysis procedure.

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Authors and Affiliations

  1. Department of Mechanical Engineering Informatics, Meiji University, Kawasaki, 214-8571, Japan

    Hiroyuki Ichihara

  2. Design Innovation Laboratory, Fujitsu Laboratories Ltd., Kawasaki, 211-8588, Japan

    Hirokazu Anai

  3. Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Hirokazu Anai

Authors
  1. Hiroyuki Ichihara
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  2. Hirokazu Anai
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Correspondence to Hiroyuki Ichihara.

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Ichihara, H., Anai, H. An SOS-QE Approach to Nonlinear Gain Analysis for Polynomial Dynamical Systems. Math.Comput.Sci. 5, 303–314 (2011). https://doi.org/10.1007/s11786-011-0095-0

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  • DOI: https://doi.org/10.1007/s11786-011-0095-0

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