Approximate Synchronization of Complex Network Consisting of Nodes With Minimum-Phase Zero Dynamics and Uncertainties

A synchronization algorithm of nonlinear complex networks composed of nonlinear nodes is designed. The main idea is to apply the exact feedback linearization of every node first, then applying methods for synchronization of linear complex networks. The nodes need not admit full exact feedback linearization, however, they are supposed to be minimum-phase systems. To achieve the synchronization of the observable parts of the nodes, an algorithm based on the convex optimization (to be specific, on linear matrix inequalities) is proposed. Then, it is demonstrated that, using the minimum-phase assumption, the non-observable part of the nodes is synchronized as well. The algorithm for synchronization of the observable parts of the nodes can be used to design a control law that is capable of maintaining stability in presence of certain variations of the control gain. Uncertainties in the parameters are also taken into account. Two examples illustrate the control design.