Mean square exponential synchronization for two classes of Markovian switching complex networks under feedback control from synchronization control cost viewpoint

This paper is concerned with mean square exponential synchronization for two classes of Markovian switching complex networks (MSCNs) under linear negative control scheme from synchronization control cost viewpoint. Two classes of MSCNs are considered. In order to analyze synchronization controllability for the two classes of MSCNs from synchronization control cost viewpoint, synchronization control cost and synchronization controllability are defined, respectively. By utilizing M-matrix properties, a novel Lyapunov function and the stochastic analysis techniques, sufficient criteria of mean square synchronization and global synchronization for the two classes of MSCNs under feedback control are derived. Three numerical examples and simulations are given to illustrate the following conclusions: (1) the two classes of MSCNs under the same linear negative feedback controller can achieve mean square exponential synchronization and global synchronization if they satisfy sufficient conditions of mean square exponential synchronization; (2) by computing synchronization control cost, we obtain that global synchronization controllability for the first class of MSCNs may perhaps stronger or poorer than that of the second class of MSCNs with time-varying delays.