Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

Natalia Bakhtadze and Igor Yadikin
Additional contact information
Natalia Bakhtadze: V.A. Trapeznikov Institute of Control Sciences, 65 Profsoyuznaya, 117997 Moscow, Russia
Igor Yadikin: V.A. Trapeznikov Institute of Control Sciences, 65 Profsoyuznaya, 117997 Moscow, Russia

Mathematics, 2021, vol. 9, issue 24, 1-16

Abstract: The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.

Keywords: Gramian method; bilinear system process identification; generalized Lyapunov equation; knowledgebase; associative search models; wavelet analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3194/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3194/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:24:p:3194-:d:699860

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().