Generalized Lax pairs for the computation of semi-invariants

Author

Menini, Laura ; Tornambé, Antonio

Author_Institution

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

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

5384

Lastpage

5389

Abstract

A Lax pair is a classical tool for the computation of first integrals of continuous-time nonlinear systems. Semi-invariants extend the concept of first integral and generalize the concept of the pair (eigenvalue, left eigenvector) of a linear mapping to the nonlinear framework, whence play the role of basic bricks for the computation of Lyapunov functions in closed-form. In this paper, it is shown how Lax pairs can be generalized to allow semi-invariants to be computed in an algebraic way. The geometric nature of this generalization allows a parallel treatment of both continuous-time and discrete-time systems.

Keywords

Lyapunov methods; continuous time systems; discrete time systems; eigenvalues and eigenfunctions; integral equations; matrix algebra; nonlinear control systems; Lyapunov functions; algebraic way; continuous-time nonlinear systems; continuous-time systems; discrete-time systems; eigenvalue; first integrals; generalized Lax pairs; geometric nature; left eigenvector; linear mapping; nonlinear framework; parallel treatment; semi-invariants computation; Barium; Eigenvalues and eigenfunctions; Integral equations; Nonlinear systems; Polynomials; Transmission line matrix methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5717624

Filename

5717624