A quadratic form representation of polynomials of several variables and its applications

1 August 1968

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control

Vol. 13 (4) , 447-448
https://doi.org/10.1109/tac.1968.1098953

Abstract

In this correspondence, a quadratic form representation of a polynomial of several variables is given. This representation is utilized to express a sufficient condition for positive definiteness of any real polynomial of severe variables in terms of the positive definiteness of a real constant matrix, directly obtainable from the coefficients of the polynomial under consideration. Examples are included to illustrate the scope of the procedure.

Keywords

POLYNOMIALS
SYMMETRIC MATRICES
SUFFICIENT CONDITIONS
STABILITY
TRANSFER FUNCTIONS
INSPECTION
MULTIDIMENSIONAL SYSTEMS
DIFFERENTIAL EQUATIONS

This publication has 1 reference indexed in Scilit:

On positive definiteness of quartic forms of two variables
IEEE Transactions on Automatic Control, 1964