On spectral decompositions of solutions to discrete Lyapunov equations
- 作者: Yadykin I.1,2
-
隶属关系:
- Trapeznikov Institute of Control Sciences
- Skolkovo Institute of Science and Technology
- 期: 卷 93, 编号 3 (2016)
- 页面: 344-347
- 栏目: Control Theory
- URL: https://journals.rcsi.science/1064-5624/article/view/223934
- DOI: https://doi.org/10.1134/S1064562416030133
- ID: 223934
如何引用文章
详细
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.
作者简介
I. Yadykin
Trapeznikov Institute of Control Sciences; Skolkovo Institute of Science and Technology
编辑信件的主要联系方式.
Email: jad@ipu.ru
俄罗斯联邦, Profsoyuznaya ul. 65, Moscow, 117997; ul. Novaya 100, Skolkovo, Moscow oblast, 143025