This article investigates the synchronization of semi-Markovian switching complex networks with partial unknown transition rates. Different from Markovian switching system, semi-Markov process is characterized by a fixed transition probability matrix and a probability density function of the sojoturn time, and the sojourn time obeys an expanded exponential distribution, which relaxes the restriction that the sojoturn time obeys memoryless exponential distribution. To realize synchronization, event-triggered control is applied which effectively reduced the control cost. It is demonstrated that the semi-Markovian switching complex networks can realize synchronization under appropriate control gain, event-triggered parameter and average sojourn time. Besides, to cope with the uncertainties that may occur during the switching process, the synchronization of the semi-Markovian switching complex networks with parameter uncertainties and external disturbances is also discussed. In the end, two simulation examples are provided to verify the feasibility of our results.
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