Abstract: To address the master-slave synchronization issue for semi-Markovian neural networks with time-varying delays using static output feedback, a static output feedback controller was designed to achieve synchronization between the slave system and the master system under the influence of time-varying delays. The semi-Markov switching process was used to model time-varying delayed neural network systems, and to characterize the sudden changes in system parameters. Compared to Markov processes, the semi-Markov processes were more general. Considering the situation where the system state couldn’t be fully obtained, the output information was used to achieve synchronization between neural networks. Utilizing Lyapunov stability theory, a delay-dependent Lyapunov functional was selected and combined with integral inequality scaling techniques to derive less conservative sufficient conditions. In the absence of a controller input matrix, the free weighting matrix technique was used to separate the system matrices from the generalized matrix of the Lyapunov functional, overcoming the conservativeness of fixed weighting matrices. Finally, the effectiveness of the controller design was verified through a numerical example. The results show that the designed controller can synchronize the time-varying delay system with the master system within 5 s even if they are initially out of sync. After eliminating the error, the control signal tends towards stability, ensuring the stochastic mean-square stability of the synchronization error system while meeting the mixed infinite/passive performance indicators, which validates the rationality of the design.