Non- Blow- Up Conditions for Riccati- type Matrix Differential and Difference Equations ∗

Abstract: We present several methods to obtain global existence results for solutions of non-symmetric Riccati matrix differential equations and for generalized or perturbed symmetric Riccati differential equations. One approach is to derive sufficient conditions ensuring that the spectral norm of the solutions remain uniformly bounded in an interval (−∞, t0] or, weaker, that the min-imal an the maximal eigenvalue of a hermitian solution remains bounded in (−∞, t0]. If however, there exists a linearizing transformation, as in the case of a non-symmetric Riccati differential equa-tion, then with the aid of an appropriate Lyapunov-type function we obtain sufficient conditions guaranteeing that no escape finite time can occur. This method also applies to non-symmetric matrix Riccati difference equations. These results, among others, can then be applied to control problems like H∞-control, Markovian Jump Linear Quadratic control, Minimal Cost Variance control and to open loop and memoryless feedback Nash games as well. 1. Introduction. We consider non-symmetric non-autonomous matrix Riccati differential equations of the for