\(H_{\infty }\) Synchronization of Complex Networks Case

This chapter investigates the problem of \(H_{\infty }\) synchronization for semi-Markov jump singularly perturbed complex network (SPCN). Compared to the Markov jump SPCN, the semi-Markov jump one is more reasonable due to the transition probability being considered to be related to the mode of the past, in which the transition rate has the property of the memoryless exponential distribution. By using the Lyapunov method and linear matrix inequality technology, some synchronization criteria are deduced to ensure the synchronization of semi-Markov jump singularly SPCN. Finally, the availability of the synchronization controller are verified by a numerical example.