Perturbation analysis of the stochastic algebraic Riccati equation

Chun Yueh Chiang, Hung Yuan Fan, Matthew M. Lin, Hsin An Chen

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this paper we study a general class of stochastic algebraic Riccati equations (SARE) arising from the indefinite linear quadratic control and stochastic H problems. Using the Brouwer fixed point theorem, we provide sufficient conditions for the existence of a stabilizing solution of the perturbed SARE. We obtain a theoretical perturbation bound for measuring accurately the relative error in the exact solution of the SARE. Moreover, we slightly modify the condition theory developed by Rice and provide explicit expressions of the condition number with respect to the stabilizing solution of the SARE. A numerical example is applied to illustrate the sharpness of the perturbation bound and its correspondence with the condition number.

Original languageEnglish
Article number580
JournalJournal of Inequalities and Applications
Issue number1
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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