Abstract
By the contraction mapping theorem and the harmonic Lyapunov equation theory, sufficient existence conditions of what we call the harmonic Riccati equations in finite-dimensional linear continuous-time periodic systems are explicated. Properties of the harmonic Riccati equations are also examined. Different from the Hamiltonian analysis, the approach reveals some analytic properties of periodic solutions of periodic matrix Riccati equations. An iterative algorithm is suggested for solving periodic matrix Riccati equations, which only involves algebraic Lyapunov equations and Fourier coefficients of periodically time-varying matrices.
