A general basis for using orthogonal functions to approximate the variables of a dynamic output feedback control system is presented. The use of an operational matrix of integration reduces the problem to a set of linear algebraic equations. The result is also useful for implementing open-loop approximation of derived closed-loop control. The flexible controller structure provides easy adaptation to feedback configurations using state, output, dynamic output or observer output, and feedback compensator. As an example, an approximation analysis of dynamic output feedback control via Fourier series is investigated.