This short remark describes some of the key points of the Floquet-Lyapunov theory of linear periodic differential systems. The basic transformation is presented, and its properties from the point of view of the source and target matrices and stability are discussed. The proposed methodology can be used in analysis, control design and simulation of systems with time-periodic characteristics. A method for designing a stabilizing state feedback control law is proposed. The methodology can be used in analysis and controller design for example in processes involving rotating machines and engines.