A Sufficient Condition for K-Controllability of Network Systems

Controllability is usually researched by combing the choose of driver nodes. This is however not sufficient for the large-scale network in engineering applications, where the state of the entire network is expected to be driven to the desired value in a given period of time. In this paper, the concept of K-Controllability is utilized to describe the controllability performance based on the traditional controllability theory. A sufficient condition of K-Controllability is proposed by extracting and controlling the information transmission links from the complex interconnections of the network. To make this condition easy to use, an algorithm is developed to convert any structure matrix of system to the form described in this condition. The effectiveness of the proposed theorem and algorithm is demonstrated in both analysis and simulations.