Controllability of linear systems subject to packet losses

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In this paper we study the controllability properties of discrete-time linear systems subject to packet losses. We tackle the problem from a switching systems perspective in which available information known on the packet loss signal, e.g., there cannot be more than a given maximum number of consecutive losses, is modelled through an automaton. For the resulting constrained switching system, we reformulate the controllability problem into an easier-to-study formulation through an algebraic characterization.We show that the particular case where the packet loss signal does not contain more than N consecutive dropouts (N G N) boils down to a similar controllability problem with switching delays previously studied in the literature. For the general case, i.e., for an arbitrary automaton describing the lossy behaviour, we exploit the algebraic characterization and establish that our controllability problem of constrained switching systems is algorithmically solvable. This latter result is obtained by connecting it with the celebrated Skolem Theorem from linear algebra.