Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation

Abstract

Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati equation. The two bounds exploit the existing sensitivity estimates for the matrix exponential and are alternative.

Cutting-Edge Monte Carlo Framework: Novel “Walk on Equations” Algorithm for Linear Algebraic Systems

“…The application of linear algebraic equations extends across a wide array of fields, demonstrating their versatility in addressing complex problems and providing essential tools for understanding, modeling, and solving diverse systems and phenomena. Here are some broader perspectives on the applications of LAEs [28][29][30][31][32].…”