Observability of Network Systems: A Critical Review of Recent Results

Observability is a property of a dynamical system that defines whether or not it is possible to reconstruct the trajectory temporal evolution of the internal states of a system from a given set of outputs (measurements). In the context of network systems, two important goals are: (i) to determine if a given set of sensor nodes is sufficient to render the network observable; and (ii) what is the best set of sensor nodes among different available combinations that provide a more accurate state estimation of the network state. Alongside Kalman’s classical definition of observability, a graph-theoretical approach to determine the observability of a network system has gathered a lot of attention in the literature despite several following works showing that, under certain circumstances, this kind of approach might underestimate, for practical purposes, the required number of sensor nodes. In this work, we review with a critical mindset the literature of observability of dynamical systems, counterpoising the pros and cons of different approaches in the context of network systems. Some future research directions for this field are discussed and application examples in power grids and multi-agent systems are shown to illustrate our main conclusions.