On distributed mode-observability of multimodal systems

Given a set of autonomous discrete-time LTI systems, one element - the current mode - is active. A number of agents identified to the nodes of a directed graph have different incomplete observations of the system's state, partial knowledge of the system's parameters and no knowledge of the initial state. A distributed scheme based on local communication among agents is studied to identify the current mode. Centralized and de-centralized distinguishability conditions are derived as well as a tight estimate of the number of steps required for the convergence of a distributed mode observer. Contingent on the information available to the agents, robustness to faulty or malicious communication is discussed. A distributed mode observer with a degree of robustness is proposed.