Accession Number:

AD0744849

Title:

The Geometry of the Riccati Equation

Descriptive Note:

Doctoral thesis

Corporate Author:

UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF AEROSPACE ENGINEERING

Personal Author(s):

• Rodriguez-Canabal, Jose M.

Report Date:

1972-06-01

Pagination or Media Count:

40.0

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.

Descriptors:

• *DIFFERENTIAL EQUATIONS
• MATRICES(MATHEMATICS)
• GEOMETRY
• CONVEX SETS
• THEOREMS
• HAMILTONIAN FUNCTIONS
• POLYNOMIALS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE