An improved version of the singularity-induced bifurcation theorem

Author

Lijun, Yang ; Yun, Tang

Author_Institution

Dept. of Math. Sci., Tsinghua Univ., Beijing, China

Volume

46

Issue

9

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

1483

Lastpage

1486

Abstract

It has been shown recently that there is a new type of codimension one bifurcation, called the singularity-induced bifurcation (SIB), arising in parameter dependent differential-algebraic equations (DAEs) of the form x˙=f and 0=g, and which occurs generically when an equilibrium path of the DAE crosses the singular surface defined by g=0 and det g_y=0. The SIB refers to a stability change of the DAE owing to some eigenvalue of a related linearization diverging to infinity when the Jacobian g_y is singular. In this article an improved version (Theorem 1.1) of the SIB theorem with its simple proof is given, based on a decomposition theorem (Theorem 2.1) of parameter dependent polynomials

Keywords

bifurcation; differential equations; matrix algebra; polynomials; singularly perturbed systems; stability; codimension one bifurcation; decomposition theorem; differential-algebraic equations; eigenvalues; equilibrium path; parameter dependent polynomials; singularity-induced bifurcation; stability; Bifurcation; Differential equations; Eigenvalues and eigenfunctions; H infinity control; Jacobian matrices; Nonlinear equations; Polynomials; Power system dynamics; Power system modeling; Stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.948482

Filename

948482