In this paper, the RCF method is used in sensitivity analysis problems of the discrete power systems including both series FACTS equipments such as TCSC in transmission lines and generator controllers such as Exciter and PSS in generator terminal. To apply the RCF method in small signal stability problems of discrete power systems, state transition equations of controllers and TCSC are derived and the sensitivity calculation algorithm using state transition equations in discrete time domain is devised. The results of eigenvalue analysis showed that the variations of eigenvalues after periodic switching operations of TCSC can be calculated exactly by the RCF method and the change of firing angles in TCSC have important effect to determine the stability of power systems.