Constructive methods for obtaining the solution of the periodic boundary value problem for a system of matrix differential equations of Riccati type (Q662453)

The authors consider the boundary value problem \[ \begin{aligned} {\frac {dX}{dt}} &= A_1(t)X+ XB_1(t)+ X(S_1(t) X+ S_2(t) Y)+ F_1(t),\\ {\frac{dY}{dt}} &= A_2(t)Y+ YB_2(t)+ Y(P_1(t) X+ P_2(t) Y)+ F_2(t),\end{aligned} \] \[ X(0)= X(\omega),\quad Y(0)= Y(\omega), \] where \((t,X,Y)\in J\times\mathbb{R}^{n\times n}\times \mathbb{R}^{n\times n}\), \(A_i,B_i,S_i,P_i,F_i\in C(J,\mathbb{R}^{n\times n})\), \(i= 1,2\), and \(J= [0,\omega]\), \(\omega> 0\). The authors obtain sufficient conditions for existence of a unique solution of problem (1) and propose an algorithm for constructing the solution.