Analytical construction of a negative semidefinite solution of algebraic Riccati equations and its application

摘要

A sufficient condition for the existence of a symmetric negative semidefinite solution of algebraic matrix Riccati equations is given, and at the same time the negative semidefinite solution is constructed by an analytical method. A few properties of the negative semidefinite solution are also investigated. It is shown that the negative semidefinite solution having those properties plays a more important role than a positive semidefinite solution in the existence problem of the solution of the corresponding Riccati differential (difference) equations. The results are applied to this existence problem.