48912

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

A Comparison of Sub-Gramian Analysis with Eigenvalue Analysis for Stability Estimation of Large Dynamical Systems

DOI: 

10.1134/S000511791810003X

Наименование источника: 

  • Automation and Remote Control

Обозначение и номер тома: 

Vol. 79, No. 10

Город: 

  • Moscow

Издательство: 

  • Pleiades Publishing, Ltd

Год издания: 

2018

Страницы: 

1767-1779
Аннотация
In earlier works, solutions of Lyapunov equations were represented as sums of Hermitian matrices corresponding to individual eigenvalues of the system or their pairwise combinations. Each eigen-term in these expansions are called a sub-Gramian. In this paper, we derive spectral decompositions of the solutions of algebraic Lyapunov equations in a more general formulation using the residues of the resolvent of the dynamics matrix. The qualitative differences and advantages of the sub-Gramian approach are described in comparison with the traditional analysis of eigenvalues when estimating the proximity of a dynamical system to its stability boundary. These differences are illustrated by the example of a system with a multiple root and a system of two resonating oscillators. The proposed approach can be efficiently used to evaluate resonant interactions in large dynamical systems.

Библиографическая ссылка: 

Ядыкин И.Б., Искаков А.Б. A Comparison of Sub-Gramian Analysis with Eigenvalue Analysis for Stability Estimation of Large Dynamical Systems // Automation and Remote Control. 2018. Vol. 79, No. 10. С. 1767-1779.

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