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

作者：Guo, Chun Hua; Yu, Bo^*

来源：Taiwanese Journal of Mathematics, 2015, 19(1): 77-89.

DOI：10.11650/tjm.19.2015.4546

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

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,infinity) 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.

• 出版日期2015-2
• 单位湖南工业大学