Pinning observability in complex networks

A new concept called pinning observability for complex networks is first proposed in this study. It is well known that in a very large-scale network, there are many nodes as well as lots of connections among the nodes. Thus, it is literally impossible to observe states of all the nodes so as to recover the network by reaching synchronisation between the original network and a newly constructed network. To reduce the number of observable nodes' states, some feedback controllers can be applied on a small fraction of the chosen nodes to realise the synchronisation. Hence, the new concept pinning observability in complex networks is introduced for this purpose. First, a general criterion for synchronisation via pinning observability in complex networks with linear coupling is given based on which the parametric regions for pinning observability are discussed. Then, some decoupled and easily verified conditions for pinning observability are derived. Furthermore, a general criterion for synchronisation via pinning observability in complex networks with non-linear coupling is given and an application to genetic regulatory networks via pinning observability is formulated. Finally, some simulation examples are given to verify the present theoretical analysis in this study.