Hermitian Riccati differential equations

This chapter is dedicated to the theory of Hermitian Riccati differential equations (HRDE), which are of importance in various fields of applications, as e.g., the linear quadratic optimal problem, differential games, differential geometry, fac­torization problems and spectral theory. Since the linear differential system that, according to Radon’s Lemma, is associated to HRDE is a linear Hamiltonian sys­tem, it turns out that the solutions of HRDE have exceptionally nice properties. In particular, the solutions depend monotonically on the coefficients and the initial data. Moreover, in the time-invariant case and for periodic coefficients (see also 5) the phase portrait of HRDE has a very special structure.