## Taiwanese Journal of Mathematics

### A CONVERGENCE RESULT FOR MATRIX RICCATI DIFFERENTIAL EQUATIONS ASSOCIATED WITH $M$-MATRICES

#### Abstract

The initial value problem for a matrix Riccati differential equation associated with an $M$-matrix is known to have a global solution $X(t)$ on $[0, \infty)$ when $X(0)$ takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as $t$ goes to infinity $X(t)$ converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this paper we present a new approach for proving the convergence, which is based on the doubling procedure and is also valid for the critical case. The approach also provides a way for solving the initial value problem and a new doubling algorithm for computing the minimal nonnegative solution of the algebraic Riccati equation.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 1 (2015), 77-89.

Dates
First available in Project Euclid: 4 July 2017

https://projecteuclid.org/euclid.twjm/1499133618

Digital Object Identifier
doi:10.11650/tjm.19.2015.4546

Mathematical Reviews number (MathSciNet)
MR3313405

Zentralblatt MATH identifier
1357.34034

#### Citation

Guo, Chun-Hua; Yu, Bo. A CONVERGENCE RESULT FOR MATRIX RICCATI DIFFERENTIAL EQUATIONS ASSOCIATED WITH $M$-MATRICES. Taiwanese J. Math. 19 (2015), no. 1, 77--89. doi:10.11650/tjm.19.2015.4546. https://projecteuclid.org/euclid.twjm/1499133618

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