Article ID Journal Published Year Pages File Type
4602976 Linear Algebra and its Applications 2006 14 Pages PDF
Abstract

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games-both stochastic and deterministic. The purpose of this paper is to prove some fundamental properties such as comparison, monotonicity and existence theorems. These properties are well known for classical Riccati differential equations when certain matrices are assumed definite. As applications, we obtain conditions for the existence of solutions to the algebraic Riccati equation and to equations with periodic coefficients.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory