On spectral decompositions of solutions to discrete Lyapunov equations
- Authors: Yadykin I.B.1,2
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Affiliations:
- Trapeznikov Institute of Control Sciences
- Skolkovo Institute of Science and Technology
- Issue: Vol 93, No 3 (2016)
- Pages: 344-347
- Section: Control Theory
- URL: https://journals.rcsi.science/1064-5624/article/view/223934
- DOI: https://doi.org/10.1134/S1064562416030133
- ID: 223934
Cite item
Abstract
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.
About the authors
I. B. Yadykin
Trapeznikov Institute of Control Sciences; Skolkovo Institute of Science and Technology
Author for correspondence.
Email: jad@ipu.ru
Russian Federation, Profsoyuznaya ul. 65, Moscow, 117997; ul. Novaya 100, Skolkovo, Moscow oblast, 143025