Controllability and Observability Preservation for Networked Systems with Time Varying Topologies

When dealing with networked systems, the concept of controllability refers to the possibility of controlling the overall state of a group of agents by providing an external input only to a subset of them, that are referred to as leaders. On the same lines, the concept of observability is related to the possibility of observing the whole state of the networked system from only a subset of the agents. In this paper we introduce a decentralized interaction rule that ensures preservation of the controllability and observability properties of a networked system. The proposed strategy is based on the fact that these properties are strongly related to the topology of the underlying communication graph. We will show that connectivity maintenance and a random choice of the edge–weights are key concepts to ensure controllability and observability preservation for a networked system.