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The D-decomposition technique for linear matrix inequalities

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Abstract

In the framework of the theory of linear matrix inequalities, a method is proposed for determining all the domains in the parameter space having the property that an affine family of symmetric matrices has the same fixed number of like-sign eigenvalues inside each of the domains. The approach leans on the ideas of D-decomposition; it is particularly efficient in the problems involving few parameters. Generalizations of the method are considered along with its modifications to the presence of uncertainty.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Science, Russian Academy of Sciences, Moscow, Russia

    B. T. Polyak & P. S. Shcherbakov

Authors
  1. B. T. Polyak
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  2. P. S. Shcherbakov
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Additional information

Original Russian Text © B.T. Polyak, P.S. Shcherbakov, 2006, published in Automatika i Telemekhanika, 2006, No. 11, pp. 159–174.

This work was supported by the Russian Foundation for Basic Research, projects nos. 05-01-00114, 05-08-01177, and the Integrated Research Program no. 22 “Control Processes” of the Presidium of the Russian Academy of Sciences.

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Polyak, B.T., Shcherbakov, P.S. The D-decomposition technique for linear matrix inequalities. Autom Remote Control 67, 1847–1861 (2006). https://doi.org/10.1134/S0005117906110063

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  • DOI: https://doi.org/10.1134/S0005117906110063

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