A closed form solution for nonsymmetric Riccati differential equations with invertible quadratic coefficient (Q810220)

For a nonsymmetric matrix Riccati differential equation with an invertible matrix coefficient in the quadratic term, an explicit formula describing the solution in a neighborhood of an initial point is derived. The result generalizes that of the first author [Syst. Control Lett. 12, 39-43 (1989; Zbl 0678.34004)]. The technique of the above paper is combined with a new exponential representation (involving an arbitrary invertible matrix) of the solution of a Cauchy problem for a second order linear stationary matrix differential equation.