Abstract: Based on the finite-frequency theory, in this study, we designed a state feedback controller for continuous-time Markov jump systems to satisfy their multiple frequency performance requirements. Due to the stochastic Markov jumping among different modes, the finite-frequency specification for deterministic systems cannot be directly used in jump systems. In this paper, by augmenting the modes of Markov jump systems, we transform the original jump systems into augmented deterministic systems with transition probabilities. Then, based on the generalized KYP lemma, we designed a state feedback controller to stabilize the jump systems to enable them to meet the multi-frequency and multi-performance requirements. The proposed methodology provides a new approach to the finite frequency problems of the hybrid generalized KYP lemma.