Observers design in complex networks: Pinning observability

In this paper, the new concept of pinning observability for complex networks and systems is discussed. Note that in a very large-scale network, there are many nodes and it is impossible to measure the states of all the nodes so as to reach synchronization between the original network and a new constructed network. To reduce the number of observable nodes, some feedback controllers are applied on the chosen nodes, which is defined as pinning observability. First, a general criterion for synchronization via pinning observability is given based on which the parametric regions for pinning observability are discussed. Then, some decoupled conditions for pinning observability are derived. Furthermore, an application to genetic regulatory networks via pinning observability is discussed. Finally, a simulation example is given to verify the theoretical analysis in this paper.