Superposition laws for solutions of differential matrix Riccati equations arising in control theory

Representation formulas are given for the general solution of the matrix Riccati equation using known solutions, with ( -representations). The 5- representation is a superposition formula, in that it expresses the general solution explicitly as a function of five particular solutions and N²arbitrary constants ( ), using no further information. The representation formulas can be used in numerical calculations. The 4- and 5- representations are specially useful when a solution has a singularity for some finite . They also clarify the properties of the solution space: the matrix elements of are meromorphic functions of having simple poles as the only possible singularities. The relation between the representation formulas and previously known results is discussed.