Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation

Vera Angelova, Mustapha Hached and Khalide Jbilou
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Vera Angelova: Department of Intelligent Systems, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Akad. G. Bonchev, Bl. 2, 1113 Sofia, Bulgaria
Mustapha Hached: Université de Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé, F-59000 Lille, France
Khalide Jbilou: Laboratoire LMPA, 50 Rue F. Buisson, ULCO Calais, CEDEX, 62228 Calais, France

Mathematics, 2021, vol. 9, issue 8, 1-18

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.

Keywords: non-linear matrix equations; perturbation bounds; Lyapunov majorants; fixed-point principle; nonsymmetric differential matrix Riccati equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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