39661

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Spectral Decomposition of Solutions to Discrete Lyapunov Equations

DOI: 

doi:10.1134/s1064562416030133

Наименование источника: 

  • Doklady Mathematics

Обозначение и номер тома: 

Vol. 93 issue 3

Город: 

  • Moscow

Издательство: 

  • Pleiades Publishing

Год издания: 

2016

Страницы: 

344-347
Аннотация
A new approach to solving discrete Lyapunov matrix algebraic equations is based on methods for spectral decomposition of their solutions. Assuming that all eigenvalues of the matrices on the left-hand side of the equation lie inside the unit disk, it is shown that the matrix of the solution to the equation can be calculated as a finite sum of matrix bilinear quadratic forms made up by products of Faddeev matrices obtained by decomposing the resolvents of the matrices of the Lyapunov equation. For a linear autonomous stochastic discrete dynamic system, analytical expressions are obtained for the decomposition of the asymptotic variance matrix of system’s states.

Библиографическая ссылка: 

Ядыкин И.Б. Spectral Decomposition of Solutions to Discrete Lyapunov Equations / Doklady Mathematics. Moscow: Pleiades Publishing, 2016. Vol. 93 issue 3. С. 344-347.