Adaptive synchronization of complex networks with neutral-type nodes

In this letter, the design problem of global asymptotical synchronization through adaptive control for a class of complex networks with time-varying delayed couplings is concerned with. In the complex networks under consideration, the dynamic of each node is expressed by a neutral-type system with time-varying delays. By using the LaSalle invariance principle and some properties of Kronecker product, a sufficient condition that globally asymptotically stabilizes the error system through adaptive control is derived, which ensures the dynamics of whole networks synchronize with the desirable synchronization manifold. In the proposed criterion, the matrices denoting the topological structure of the complex networks are not need to be symmetric. And the adaptive feedback strength is updated based on both the current and the delayed state errors of the networks. A numerical example is presented to show the effectiveness and applicability of the proposed approach.