A procedure for the computation of semi-invariants

Author

Menini, Laura ; Tornambè, Antonio

Author_Institution

Dipt. di Inf., Sist. e Produzione, Univ. di Roma Tor Vergata, Rome, Italy

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

7460

Lastpage

7465

Abstract

This paper deals with the concept of semi-invariant (Darboux polynomial), which extends to the nonlinear case the concept of eigenfunction. Semi-invariants can be used as elementary bricks for the construction of Lyapunov functions. For planar systems, the construction of semi-invariants is strictly correlated with the existence of an orbital symmetry of the system. This feature is not easily extended when the dimension of the system state is greater than 2. In this paper, a procedure is proposed that does not rely on the existence of orbital symmetries of the system, whence can be easily applied to general systems. The proposed technique is applied to some relevant and physically motivated systems.

Keywords

Lyapunov methods; eigenvalues and eigenfunctions; polynomials; Darboux polynomial; Lyapunov functions; eigenfunction; elementary bricks; orbital symmetry; planar systems; semiinvariants computation; Eigenvalues and eigenfunctions; Jacobian matrices; Linear systems; Lyapunov method; Poles and zeros; Polynomials; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400709

Filename

5400709