Metelitsyn´s inequality and stability criteria in mechanical problems

Author

Seyranian, A.P. ; Kliem, W.

Author_Institution

Inst. of Mech., Moscow State Lomonosov Univ., Russia

Volume

4

fYear

2003

fDate

20-22 Aug. 2003

Firstpage

1096

Abstract

Asymptotic stability criteria for general linear mechanical systems are studied. It is shown that the inequality first derived by Metelitsyn (1952) is a sufficient but not a necessary condition for asymptotic stability. We argue that this inequality is of little use in applications. The theorems of Metelitsyn based on his inequality as well as critical comments in the literature on these theorems are analyzed. Practical sufficient stability criteria are obtained in terms of extreme eigenvalues of the system matrices. This analysis is of special value for rotor systems in a complex setting, which is demonstrated by three examples.

Keywords

asymptotic stability; eigenvalues and eigenfunctions; linear systems; matrix algebra; mechanical stability; rotors; Metelitsyn inequality; Metelitsyn stability criteria; asymptotic stability; extreme eigenvalues; general linear mechanical systems; rotor systems; system matrices; Asymptotic stability; Damping; Eigenvalues and eigenfunctions; Linear matrix inequalities; Mathematics; Petroleum; Polynomials; Stability analysis; Stability criteria; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Physics and Control, 2003. Proceedings. 2003 International Conference

Print_ISBN

0-7803-7939-X

Type

conf

DOI

10.1109/PHYCON.2003.1237058

Filename

1237058