A TIME DOMAIN CHARACTERIZATION OF RATIONAL POSITIVE-REAL MATRICES.

Abstract

Let w(t) denote the distributional inverse Laplace transform of a rational function W(s), where the corresponding region of convergence is taken to be a half-plane extending infinitely to the right. In addition it is assumed that w(t) is an ordinary function that satisfies certain conditions on its integrability, then it is shown that a necessary and sufficient condition for W(s) to be positive-real is that the even part of w(t) be a nonnegative-definite function. Necessary and sufficient conditions are established, which characterize the universe Laplace transform of W(s) in terms of nonnegativedefinite distribution and their orders. A similar result for positive-real matrices is given. The two theorems give a complete time-domain characterization of lumped linear fixed finite and passive n-ports. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 05, 1963
Accession Number
AD0430564

Entities

People

  • A. H. Zemanian

Organizations

  • State University of New York

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Complex Variables
  • Convergence
  • Functions (Mathematics)
  • Mathematical Analysis
  • Rational Functions
  • Time Domain

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.