Analysis of the second order matrix Riccati equations (Q1064449)

The author considers the equation \[ (1)\quad \dot P(t)=AP(t)+P(t)A^ T- P(t)RP(t)+Q,\quad P(0)=P_ 0 \] where A,R,Q and \(P_ 0\) are \(n\times n\) real constant matrices and simplifies the verification of a necessary and sufficient condition obtained in his earlier work for existence of periodic solutions of (1) to special cases. Examples are given for existence of a periodic solution when the matrix A has complex eigenvalues, provided \(P_ 0\) is suitably chosen.