Sensitivity analysis of the differential matrix Riccati equation based on the associated linear differential system (Q1373122)

The solution to the differential matrix Riccati equation (DMRE) arising in the theory of linear-quadratic optimization and optimal filtering is usually contaminated with rounding and parameter errors. This may lead to significant loss of accuracy and, in particular, to breaking of symmetry and divergence of the numerical procedure carried out in floating-point computing environment. In turn, the actual error in the computed solution depends on the sensitivity of the solution of DMRE to perturbation in its matrix coefficients. Hence obtaining perturbation bounds for DMRE is important from both the theoretical and computational point of view. The authors give an improved perturbation bounds for the solution of the \(n\)th order DMRE using the associated linear \(2n\)th order differential system. The new bounds are alternative to those existing in the literature and are sharper in some cases. Moreover the estimate proposed in this paper has the advantage that it is not related with the solution to the DMRE and hence with the problem of possible loss of symmetry and divergence of the numerical procedure.