Synchronization criteria for singular complex networks with Markovian jump and time-varying delays via pinning control

This paper makes a study on the problem of synchronization for singular complex networks with Markovian jumping parameters and mixed time-delays. The system consists of N nodes which switch from one mode to another according to a Markovian chain with known transition probability. Based on the strategies of pinning control, the singular complex networks are synchronized. A new type of criterion for synchronization can be obtained by means of utilizing the appropriate Lyapunov-Krasovskii function, the linear matrix inequality (LMI) approach, stochastic analysis techniques and the convexity of matrix functions. Finally, simulation examples are employed to demonstrate the effectiveness of the proposed method.