I. B. Yadykin, “On properties of gramians of continuous control systems”, Avtomat. i Telemekh., 2010, no. 6, 39–50; Autom. Remote Control, 71:6 (2010), 1011

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Avtomatika i Telemekhanika, 2010, Issue 6, Pages 39–50 (Mi at828)

This article is cited in 37 scientific papers (total in 37 papers)

Deterministic Systems

On properties of gramians of continuous control systems

I. B. Yadykin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Full-text PDF (215 kB) Citations (37)

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Abstract: A new approach to the study of controllability and observabihty by means of analysis of the controhabihty and observabihty matrices and gramians was proposed. It rehes on the lemma of expansion of the matrix integrals proved by expanding the resolvents of the matrices $A_m$, and $A$ and the properties of convolution of the matrix function in the complex domain. Analysis of the structural properties of gramians demonstrated that the coefficients of the characteristic equations and the Faddeev matrices in the decomposition of the resolvent of the system dynamics matrix play the leading part in their formation. An example illustrating the properties of gramians was given.

Presented by the member of Editorial Board: A. P. Kurdyukov

Received: 15.12.2009

English version:
Automation and Remote Control, 2010, Volume 71, Issue 6, Pages 1011–1021
DOI: https://doi.org/10.1134/S0005117910060032

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: I. B. Yadykin, “On properties of gramians of continuous control systems”, Avtomat. i Telemekh., 2010, no. 6, 39–50; Autom. Remote Control, 71:6 (2010), 1011–1021

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/at828

https://www.mathnet.ru/eng/at/y2010/i6/p39

This publication is cited in the following 37 articles:

D. E. Kataev, “Perspektivy razvitiya modalnogo analiza po Lyapunovu na osnove dannykh izmerenii”, UBS, 110 (2024), 295–309
Dmitry E. Kataev, Evgeny Y. Kutyakov, “Structurally Constrained Fuzzy Selective LQ WADC Based on the Spectral Decomposition of Gramians”, IFAC-PapersOnLine, 58:13 (2024), 350
D. E. Kataev, E. Yu. Kutyakov, “Modalnyi analiz po lyapunovu na osnove izmerenii s pomoschyu proni-analiza”, UBS, 104 (2023), 100–117
I. B. Yadykin, I. A. Galyaev, “Strukturnye spektralnye metody resheniya nepreryvnykh uravnenii Lyapunova”, Avtomat. i telemekh., 2023, no. 12, 18–37
I. B. Yadykin, I. A. Galyaev, “Structural Spectral Methods for Solving Continuous Lyapunov Equations”, Autom Remote Control, 84:12 (2023), 1259
Igor Yadykin, “Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms”, Mathematics, 10:13 (2022), 2339
Alexey B. Iskakov, Nikita V. Tomin, Igor B. Yadykin, Daniil A. Panasetsky, Evgeniy Yu. Kutyakov, Nikolai I. Voropai, “Selective LQ wide area damping of power networks based on the spectral decomposition of Gramians”, IFAC-PapersOnLine, 55:9 (2022), 152
Iskakov A.B., Yadykin I.B., “Lyapunov Modal Analysis and Participation Factors Applied to Small-Signal Stability of Power Systems”, Automatica, 132 (2021), 109814
Bakhtadze N., Yadykin I., Maximov E., Maximova N., Chereshko A., Vershinin Y., “Forecasting the Risks of Stability Loss For Nonlinear Supply Energy Systems”, IFAC PAPERSONLINE, 54:1 (2021), 478–483
N. I. Voropai, I. I. Golub, D. N. Efimov, A. B. Iskakov, I. B. Yadykin, “Spectral and modal methods for studying stability and control of electric power systems”, Autom. Remote Control, 81:10 (2020), 1751–1774
Bakhtadze N. Yadikin I., “Discrete Predictive Models For Stability Analysis of Power Supply Systems”, Mathematics, 8:11 (2020), 1943
Yadykin I.B. Iskakov A.B., “Spectral Decompositions For the Solutions of Lyapunov Equations For Bilinear Dynamical Systems”, Dokl. Math., 100:2 (2019), 501–504
Nikita Tomin, Daniil Panasetsky, Alexey Iskakov, C. Rehtanz, N. Voropai, “Stability of Power Grids: State-of-the-art and Future Trends”, EPJ Web Conf., 217 (2019), 01017
Evgeniy J. Kutyakov, Sergey V. Dushin, Alexey B. Iskakov, Alexander N. Abramenkov, 2019 Twelfth International Conference “Management of large-scale system development” (MLSD), 2019, 1
Iskakov A.B., “Integral Solution of Linear Multi-Term Matrix Equation and Its Spectral Decompositions”, Dokl. Math., 97:2 (2018), 193–196
I. B. Yadykin, A. B. Iskakov, “Comparison of sub-Gramian analysis with eigenvalue analysis for stability estimation of large dynamical systems”, Autom. Remote Control, 79:10 (2018), 1767–1779
Yadykin I.B., “Optimal Synthesis of the Low-Order Model Parameters For a Large-Scale Energy System on the Basis of the Gramians Spectral Decomposition”, IFAC PAPERSONLINE, 51:28 (2018), 7–12
Iskakov A.B. Lavrikov A.V. Yadykin I.B., “Fast Calculation of Modal Interaction in Large Power Systems Using Spectral Decompositions of Gramians”, IFAC PAPERSONLINE, 51:28 (2018), 564–569
Vassilyev S.N. Yadykin I.B. Iskakov A.B. Kataev D.E. Grobovoy A.A. Kiryanova N.G., “Participation Factors and Sub-Gramians in the Selective Modal Analysis of Electric Power Systems”, IFAC PAPERSONLINE, 50:1 (2017), 14806–14811
Kiryanova N., “Comparison of Two Methods of Power Systems Stability Degree Assessment”, 2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), IEEE, 2017

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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