Subspace method for the estimation of large-scale structured real stability radius

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456011" target="_blank" >RIV/00216208:11320/22:10456011 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lQ6C5C2W3J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lQ6C5C2W3J</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-022-01340-9" target="_blank" >10.1007/s11075-022-01340-9</a>

Result language

angličtina

Original language name

Subspace method for the estimation of large-scale structured real stability radius

Original language description

We consider the autonomous dynamical system x &apos;= This linear dynamical system is asymptotically stable if all of the eigenvalues of A lie in the open left-half of the complex plane. In this case, the matrix A is said to be Hurwitz stable or shortly a stable matrix. In practice, the stability of a system can be violated because of perturbations such as modeling errors. In such cases, one deals with the robust stability of the system rather than its stability. The system above is said to be robustly stable if the system, as well as all of its perturbations from a certain perturbation class, are stable. To measure the robustness of the system subject to perturbations, a quantity of interest is the stability radius or in other words the distance to instability. In this paper, we focus on the estimation of the structured real stability radius for large-scale systems. We propose a subspace framework to estimate the structured real stability radius and prove that our new method converges at a quadratic rate in theory. Our method benefits from a one-sided interpolatory model order reduction technique, in the sense that the left and the right subspaces are the same. The quadratic convergence of the method is due to the certain Hermite interpolation properties between the full and reduced problems. The proposed framework estimates the structured real stability radius for large-scale systems efficiently. The efficiency of the method is demonstrated on several numerical experiments.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Numerical Algorithms

ISSN

1017-1398

e-ISSN

1572-9265

Volume of the periodical

92

Issue of the periodical within the volume

2

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

22

Pages from-to

1289-1310

UT code for WoS article

000817851100002

EID of the result in the Scopus database

2-s2.0-85133003046