The matrix Riccati differential equation and the semi-group of linear fractional transformations

The matrix Riccati differential equation is discussed, from the point of view of dissipativity or conservativity of its solutions. A survey is given of results relating to analytic properties of these solutions and to the geometry of the corresponding semigroup of matrix linear fractional transformations; further, a probabilistic interpretation is given of the properties of being dissipative or conservative, and the connection between dissipativity of the solutions of the Riccati equation and the stability of the screw method is studied. Physical and technical applications of the mathematical theory are given.
There are 87 references.