Partial Cluster Stabilization and Partial Cascade Stabilization of Physical Networks

Abstract This paper defines the notions of partial cluster stability and partial cascade stability of physical network systems, develops some distributed hybrid network control techniques to achieve partial cluster stabilization and partial cascade stabilization, and applies the proposed approaches to a power network system model. Partial cluster stability is the property that every subsystem in a physical network system is partially convergent, and at least one subsystem is partially semistable. Partial cascade stability is the property of damping disturbance propagation of the physical network system. To achieve the effects of partial cluster stability and partial cascade stability, some distributed hybrid network controller architectures with both distributed feedbacks and distributed resetting laws are proposed. In the proposed controller architectures, each plant is connected to a controller node with one communication link, and the controller nodes form a connected controller graph which collects information from plants and returns feedback information. To show the efficacy of the proposed approach, the proposed hybrid control techniques are applied to a power network system model.