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# Accession Number:

## AD0600737

# Title:

## MATRIX RICCATI DIFFERENTIAL EQUATIONS.

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1964-03-01

# Pagination or Media Count:

##
16.0

# Abstract:

## The scalar Riccati equation y pt Y to the second power qt yrt has the following well-known properties I If one solution is known, the complete solution is obtainable by two quadratures II If two solutions are known, the complete solution is obtainable by one quadrature III The crossratio of any four distinct solutions is constant. The scalar Riccati equation has been generalized to systems. Adoption of one or the other of two particular viewpoints leads to the matrix equations u Au - u alpha u u is n x 1 and Y KY L - YMY - YN Y is n x m. This paper shows that there is an expression for the complete solution of equations of the first type, and that an expression for the complete solution of equations of the second type can be obtained by quadratures from the complete solution of the first type. Following this, properties corresponding to II and III are established for the first equation. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#