A Geometric View of the Matrix Riccati Equation

Abstract

This is a tutorial paper which describes a “geometric approach” to the description of the phase portrait of the Riccati differential equation. As such, no new results are presented. Our intention is to show how the geometric viewpoint gives insight into many of the properties of the Riccati differential equation. It is not our purpose to present a comprehensive exposition of all that is presently known on the subject Instead, we will willingly make (mostly) generic assumptions and focus on the properties of the differential equation under these simplifying assumptions. For more details, some generalizations and additional references, the reader is referred to the papers [4.14] (time-invariant coefficients) and [4.13] (periodic coefficients).