Global Robust Stability and Synchronization of Networks With Lorenz-Type Nodes

This brief addresses in a unified framework both global robust stability and synchronization problems for a class of directed networks with Lorenz-type nodes. When the key parameter in the node equation is modified, it covers the Lorenz, Chen, and Lu types of networks as special cases. Based on an observation about some special nonlinear characteristics of Lorenz-type systems, simple conditions are derived for global stability and synchronization of such networks, where the typical Lipschitz-type condition for nonlinear functions is not needed. By combining the pinning control strategy and a new linear control law, synchronization of a network with different nodes can be achieved. Several examples are given for illustration.