A method to determine whether two polynomials are relatively prime

1 June 1970

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

Vol. 15 (3) , 379-380
https://doi.org/10.1109/tac.1970.1099465

Abstract

In this paper, it is established that a necessary and sufficient condition for two monic polynomials f(\lambda) and g(\lambda) to have a common root is that \det [f(B)] = 0 or \det [g(A)] = 0 , where A and B are, respectively, the companion matrices associated with f(\lambda) and g(\lambda) . The simplicity of this method is illustrated by examples.

Keywords

POLYNOMIALS
AUTOMATIC CONTROL
STABILITY
CONTROL SYSTEMS
SUFFICIENT CONDITIONS
LYAPUNOV METHOD
SYSTEM TESTING

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