Positive Diagonal Solutions to the Lyapunov Equations.

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 = AD+DA(transform) 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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA038947

Entities

People

  • A. Berman
  • G. P. Barker
  • R. J. Plemmons

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Complex Numbers
  • Computer Science
  • Consistency
  • Determinants (Mathematics)
  • Economics
  • Eigenvalues
  • Equations
  • Inequalities
  • Mathematics
  • Matrix Theory
  • Military Research
  • Numbers
  • Numerical Analysis
  • Theorems
  • Two Dimensional
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Statistical inference.