On observability in networked control systems with packet losses

This paper deals with observability properties of networked control systems subject to packet losses. We employ a switching systems perspective in which available information on the packet loss signal, e.g., there can be at most a pre-specified number of consecutive losses, is modelled through an automaton. Based on this perspective we address several natural extensions envisioned in [7]. Our specific contributions are as follows. Firstly, we show that the method introduced in [7] in the context of controllability of linear systems subject to packet losses extends to the question of observability. The proposed characterization is necessary and sufficient as well as algorithmically verifiable. For the observability problem, our proof is valid also for non-invertible matrices, thereby improving upon the previous results in [7]. Secondly, we show that the model employed for our analysis encompasses the model of wireless control networks with switching delays introduced in [6] (though at a cost of exponential encoding). We raise several open questions related to the algebraic nature of the problem under consideration.