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Analysis of stability and stabilization of nonlinear systems via decomposition

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Abstract

We establish necessary and sufficient conditions for the solvability of a Lyapunov-type system of PDEs in the class of homogeneous functions. Using these, we propose an approach to studying the stability of an equilibrium of an essentially nonlinear system of ODEs in the critical case of n zero roots and n pure imaginary roots. The approach bases on decomposition of the system in question into two separate subsystems of half dimension.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. Yu. Aleksandrov & A. P. Zhabko

  2. Institute for System Dynamics and Control Theory, Irkutsk, Russia

    A. A. Kosov

Authors
  1. A. Yu. Aleksandrov
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  2. A. P. Zhabko
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  3. A. A. Kosov
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Corresponding author

Correspondence to A. Yu. Aleksandrov.

Additional information

Original Russian Text Copyright © 2015 Aleksandrov A.Yu., Zhabko A.P., and Kosov A.A.

St. Petersburg; Irkutsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 6, pp. 1215–1230, November–December, 2015; DOI: 10.17377/smzh.2015.56.602.

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Aleksandrov, A.Y., Zhabko, A.P. & Kosov, A.A. Analysis of stability and stabilization of nonlinear systems via decomposition. Sib Math J 56, 968–981 (2015). https://doi.org/10.1134/S0037446615060026

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  • DOI: https://doi.org/10.1134/S0037446615060026

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