Gramians Method in Researches of the Model Order Reduction and Dynamic LTI system Stability Problems

Autor:	Andrey A. Grobovoy, Valery Afanasyev, Igor B. Yadykin
Rok vydání:	2013
Předmět:	Lyapunov function Discrete mathematics Bilinear interpolation General Medicine Controllability LTI system theory symbols.namesake Matrix (mathematics) Computer Science::Systems and Control symbols Applied mathematics Observability Matrix exponential Sylvester equation Mathematics
Zdroj:	IFAC Proceedings Volumes. 46:178-183
ISSN:	1474-6670
DOI:	10.3182/20130204-3-fr-2033.00043
Popis:	This paper provides a new approach to computing infinite and finite time Gramians and cross-Gramians relying on the use of the Laplacian transformation to matrix exponential time functions and expansion of the product of these functions. The expansions are bilinear and quadratic forms for sequences of Faddeev matrices generated by resolvents of original matrices. Matrix identities are obtained for bilinear and quadratic forms of these Faddeev sequences. Asymptotic expansions are found for expansion of Controllability and Observability Gramians of dynamic systems under control modes at time preceding the system arriving at the stability boundary. The common fact lies in the approach foundations: Controllability, Observability and Cross –Gramians may be represented as a quadratic or bilinear matrix forms sum, to be generated by the Lyapunov or Sylvester equation matrices.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::308a88c2498444d7868bfc053d4cede5 https://doi.org/10.3182/20130204-3-fr-2033.00043 Zobrazit plný text záznamu