Differential inequalities and the matrix Riccati equation

Abstract

The matrix Riccati equation has attracted attention recently because of its occurrence in a number of different situations. Its solutions determine solutions of the optimal linear regulator problem; the existence of solutions on an interval is related to disconjugacy of a linear Hamiltonian system on an interval has demonstrated an equivalence between solutions of matrix Riccati equations and Fredholm resolvents. Most recently, Fair has written about continued fraction solutions of a Riccati equation in a Banach algebra.