Bounded solutions of a class of Riccati matrix equations (Q1382905)

The paper deals with the Riccati matrix equation \[ {dp\over dt}+ p^2= Q(t),\quad 0\leq t<\infty.\tag{1} \] The right-hand side is a square \(m\)-dimensional continuous matrix-valued function with nonpositive nondiagonal terms, satisfying the following conditions \[ \sum^m_{j= 1} Q_{ij}\geq 0;\quad 0<\sup_t Q_{ij}(t)<\infty,\quad i=1,2,\dots,m. \] The main result may be formulated as follows: Equation (1) has a bounded solution on \([0,\infty)\) with nonnegative nondiagonal terms, and \[ \sum^m_{j= 1} p_{ij}\leq 0,\quad i=1,2,\dots,m. \]