Pinning synchronization of complex networks with time-varying coupling strength varying in a range

This paper is concerned with the pinning synchronization problem for a class of complex networks with time-varying coupling strength. Different from the traditional assumptions on coupling strength, not only the lower bound of coupling strength but also its upper bound are considered simultaneously, which means the coupling strength cannot take any value but has a upper bound. A new model for such complex networks is first established, whose coupling strength varies in two bounded subintervals with some probabilities respectively. Instead of using time-varying coupling strength signal in controller, a new kind of local state feedback controller to a small faction of network nodes is proposed, where only the bounds and probability of coupling strength are included. When the probability is unavailable, two classes of adaption laws are developed to estimate such unknown probability, which guarantee the global synchronization of complex networks. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.