Solution of the Lyapunov matrix differential equations by the frequency method
- Authors: Kataev D.E.1, Yadykin I.B.1
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Affiliations:
- Trapeznikov Institute of Control Sciences
- Issue: Vol 55, No 6 (2016)
- Pages: 843-855
- Section: Stability
- URL: https://journals.rcsi.science/1064-2307/article/view/219745
- DOI: https://doi.org/10.1134/S1064230716050063
- ID: 219745
Cite item
Abstract
Methods for solving the Lyapunov matrix differential and algebraic equations in the time and frequency domains are considered. The solutions of these equations are finite and infinite Gramians of various forms. A feature of the proposed new approach to the calculation of Gramians is the expansion of the Gramians in a sum of matrix bilinear or quadratic forms that are formed using Faddeev’s matrices, where each form is a solution of the linear differential or algebraic equation corresponding to an eigenvalue of the matrix or to a combination of such eigenvalues. An example illustrating the calculation of finite and infinite Gramians is discussed.
About the authors
D. E. Kataev
Trapeznikov Institute of Control Sciences
Author for correspondence.
Email: dekataev@gmail.com
Russian Federation, Profsoyuznaya ul. 65, Moscow, 117997
I. B. Yadykin
Trapeznikov Institute of Control Sciences
Email: dekataev@gmail.com
Russian Federation, Profsoyuznaya ul. 65, Moscow, 117997