Accession Number:

ADA038947

Title:

Positive Diagonal Solutions to the Lyapunov Equations.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1977-01-01

Pagination or Media Count:

18.0

Abstract:

This document studies various stability type conditions on a matrix A related to existence of a positive diagonal matrix D such that the Lyapunov matrix Q ADDAtransform is positive definite. Such problems arise in mathematical economics, in the study of time-invariant continuous-time systems and in the study of predator-prey systems. Using a theorem of the alternative, a characterization is given for all A such that a corresponding D exists. In addition, some necessary conditions for consistency and some related ideas are discussed. Finally, a method for constructing D is given for matrices A satisfying certain conditions.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE