**5. Conclusions**

In this paper, a nonlocal sensitivity analysis of the nonsymmetric differential matrix Riccati equation is presented. Two computable perturbation bounds are derived using the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principles, developed in [14]. The first bound is based on the integral form of the solution. The second one exploits the statement of the classical Radon's theory of local equivalence of the solution to the differential matrix Riccati equation to the solution of the initial value problem of the associated differential system. It has the advantage of not being related with the solution of the NDRE and hence with problems of divergence of the numerical procedure. Numerical examples show that the estimates proposed are fairly sharp for both low-dimensional and large-scale NDRE. The perturbation bound is a crucial issue of the process of numerical solution of an equation as well as a tool to evaluate the stability of the computation process. The tight perturbation bounds, proposed in the paper, allow estimation of the accuracy of the solution to a numerically solved nonsymmetric differential matrix Riccati equation.

**Author Contributions:** Conceptualization, V.A. and K.J.; methodology, V.A. and K.J. ; software, M.H.; validation, V.A., M.H. and K.J.; writing—original draft preparation, V.A., M.H. and K.J.; writing— review and editing, V.A., M.H. and K.J.; visualization, V.A., M.H. and K.J.; supervision, K.J.; project administration, V.A., M.H. and K.J.; funding acquisition, V.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially supported by gran<sup>t</sup> BG PLANTNET "Establishment of national information network genbank—Plant genetic resources".

**Acknowledgments:** Mustapha Hached acknowledges support from the Labex CEMPI (ANR-11- LABX-0007-01).

**Conflicts of Interest:** The authors declare no conflict of interest.
