The Geometry of the Riccati Equation

Abstract

A study of the matrix Riccati equation is presented without assuming that Q is positive semi-definite. For the autonomous case, a general existence theorem for the equilibrium points of the Riccati: equation is proven and their structure is given with respect to the partial ordering induced by the positive semi-definite matrices. Further, a method for finding all equilibria is demonstrated. Necessary and sufficient conditions are given for a global existence of the solution of the Riccati equation, as a function of the initial condition. In the time dependent case, the domain of global existence is shown to contain a certain cone.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1972
Accession Number
AD0744849

Entities

People

  • Jose M. Rodriguez-canabal

Organizations

  • University of Southern California

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Computations
  • Convex Sets
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Geometry
  • Identities
  • Intervals
  • Military Research
  • Numbers
  • Perturbation Theory
  • Polynomials
  • Real Numbers
  • Riccati Equation
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra