# Non-Symmetric Matrix Riccati Equations

### Gerhard Freiling

Universität Duisburg-Essen, Germany### G. Jank

RWTH Aachen, Germany

## Abstract

We prove a fundamental representation formula for all solutions of the matrix Riccati differential equation and of the corresponding algebraic Riccati equation. This formula contains the complete information on the phase portrait of the matrix equation and on the structure of the set F of all solutions of the corresponding algebraic equation. In particular we describe all constant, periodic and almost-periodic solutions of the matrix Riccati differential equation. Further we give an application of the fundamental representation formula to the investigation of non-autonomous Riccati equations.

## Cite this article

Gerhard Freiling, G. Jank, Non-Symmetric Matrix Riccati Equations. Z. Anal. Anwend. 14 (1995), no. 2, pp. 259–284

DOI 10.4171/ZAA/675