Necessary and sufficient conditions for the positive definiteness and stability of symmetric interval matrices

Author

Liu, Wei

Author_Institution

Sch. of Electron. & Inf. Eng., Univ. of Sci. & Technol. Liaoning, Anshan, China

fYear

2009

fDate

17-19 June 2009

Firstpage

4574

Lastpage

4579

Abstract

This paper considers the positive definiteness and stability of symmetric interval matrices. The concepts of variable nonnegative quadratic forms and intermediate separate combination are introduced, and sufficient condition for the positive definiteness of variable nonnegative quadratic forms is derived. They are applied to the positive definiteness problems of symmetric interval matrices so that necessary and sufficient conditions for the positive definiteness of symmetric interval matrices are derived. Based on some properties of positive definite matrices, necessary and sufficient conditions for the stability of symmetric interval matrices are proposed. Some examples are given to demonstrate the applicability of the derived results.

Keywords

matrix algebra; intermediate separate combination; positive definiteness problems; symmetric interval matrices; variable nonnegative quadratic forms; Eigenvalues and eigenfunctions; Stability; Sufficient conditions; Symmetric matrices; Testing; Intermediate separate combination; Positive definiteness; Stability; Symmetric interval matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference, 2009. CCDC '09. Chinese

Conference_Location

Guilin

Print_ISBN

978-1-4244-2722-2

Electronic_ISBN

978-1-4244-2723-9

Type

conf

DOI

10.1109/CCDC.2009.5191513

Filename

5191513