Lyapunov-type functions and invariant sets for Riccati matrix differential equations

We present two different methods to obtain global existence results for solutions of nonsymmetric Riccati matrix differential equations. In the first approach we derive sufficient conditions ensuring that the spectral norm of the solutions remains uniformly bounded in an interval (-∞, to]: in a second part we make use of the linearizability of the Riccati matrix differential equation. With the aid of an appropriate Lyapunov-type function we obtain sufficient conditions guaranteeing that no finite escape time of solutions can occur. These results are then applied to open loop Nash strategies as well as to H_∞-type and related Riccati differential equations. A complete solution of a problem from [ThVo] is obtained and two examples show how the methods work.