A convergence result for matrix Riccati differential equations associated with M-matrices

Date
2014-04-22
Authors
Guo, Chun-Hua
Yu, Bo
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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,∞) 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.

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Keywords
Riccati differential equation, M-matrix, Global solution, Convergence, Doubling algorithm, Algebraic Riccati equation, Minimal nonnegative solution
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