Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping. (Q1413195)

The authors consider a class of coupled matrix nonlinear differential equations which include as a particular case the matrix differential equations. The study is focussed on the existence and uniqueness of the stabilizing and bounded solutions and the existence of a maximal solution (or minimal solution) with respect to some family of global solutions of the considered equations. It is proved that, if the coefficients of the equations are periodic functions, then both the stabilizing and bounded solutions, the maximal solutions and minimal solutions are periodic functions, too.