Monotonicity and convexity properties of matrix Riccati equations
Gerhard Freiling · IMA Journal of Mathematical Control and Information · 2001
Using a Fréchet-derivative-based approach some monotonicity, convexity/concavity and comparison results concerning strictly unmixed solutions of continuous- and discrete-time algebraic Riccati equations are obtained; it turns out that these solutions are isolated and smooth functions of the input data. Similarly, it is proved that the solutions of initial value problems for both Riccati differential and difference equations are smooth and monotonic functions of the input data and of the initial value. They are also convex or concave functions with respect to certain matrix coefficients.