Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 2

Perturbation analysis of rational Riccati equations

Pages: 349 – 373



Peter Chang-Yi Weng (Guangdong–Taiwan College of Industrial Science and Technology, Dongguan University of Technology, Guangdong, China)


In this paper, we consider the perturbation analyses of the continuous-time rational Riccati equations using the norm-wise, mixed and component-wise analyses, which arises from the stochastic $H_\infty$ problems and the indefinite stochastic linear quadratic control problems. We derive sufficient conditions for the existence of stabilizing solutions of the perturbed rational Riccati equations. Moreover, we obtain the perturbation bounds for the relative errors with respect to the stabilizing solutions of the rational Riccati equations under three kinds of perturbation analyses. Numerical results are presented to illustrate sharper perturbation bounds under the normwise, mixed and componentwise perturbation analyses.


rational Riccati equation, perturbation bound, mixed condition number, component-wise perturbation analysis, stochastic optimal control

2010 Mathematics Subject Classification

15A24, 47H10, 65F35, 93C05, 93E20

Received 8 July 2020

Accepted 26 September 2020

Published 13 October 2020