Monotonicity and convexity properties of matrix Riccati equations

Using a Fréchet-derivative-based approach some monotonicity,convexity/concavity and comparison results concerning strictlyunmixed solutions of continuous- and discrete-time algebraicRiccati equations are obtained; it turns out that these solutionsare isolated and smooth functions of the input data. Similarly,it is proved that the solutions of initial value problems forboth Riccati differential and difference equations are smoothand monotonic functions of the input data and of the initial value. They are also convex or concave functions with respectto certain matrix coefficients.