Consensus over Clustered Networks Using Intermittent and Asynchronous Output Feedback

Distributed consensus protocols provide a mechanism for spreading information within clustered networks, allowing agents and clusters to make decisions without requiring direct access to the state of the ensemble. In this work, we propose a strategy for achieving system-wide consensus in the states of identical linear time-invariant systems coupled by an undirected graph whose directed sub-graphs are available only at sporadic times. Within this work, the agents of the network are organized into pairwise disjoint clusters, which induce sub-graphs of the undirected parent graph. Some cluster sub-graph pairs are linked by an inter-cluster sub-graph, where the union of all cluster and inter-cluster sub-graphs yields the undirected parent graph. Each agent utilizes a distributed consensus protocol with components that are updated intermittently and asynchronously with respect to other agents and inter-clusters. The closed-loop ensemble dynamics is modeled as a hybrid system, and a Lyapunov-based stability analysis yields sufficient conditions for rendering the agreement subspace (consensus set) globally exponentially stable. Furthermore, an input-to-state stability argument demonstrates the consensus set is robust to a large class of perturbations. A numerical simulation considering both nominal and perturbed scenarios is provided for validation purposes.