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Article Dans Une Revue IEEE Transactions on Control of Network Systems Année : 2019

Input and State Observability of Network Systems with Time-Varying Topology

Sebin Gracy
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Federica Garin
Alain Kibangou

Résumé

We aim to study the problem of reconstructing the initial state as well as the sequence of unknown inputs (ISO) for linear network systems having time-varying topology. Evolution of such systems can be represented by a collection of graphs {G k }. We find conditions under which the system with a pattern of fixed zeros imposed by {G k } is ISO: a) for almost all choices of edge weights in {G k } (structural ISO); and b) for all non-zero choices of edge weights in {G k } (strongly structural ISO). We introduce two suitable descriptions of the whole collection of graphs {G k } named as dynamic graph and dynamic bipartite graph. Two equivalent characterizations of structural ISO are then stated in terms of existence of a linking and a matching of suitable size in the dynamic graph and in the dynamic bipartite graph, respectively. For strongly structural ISO, we provide a sufficient condition and a necessary condition, both concerning the existence of a uniquely restricted matching of suitable size in the dynamic bipartite graph and in a subgraph of it. When there is no direct feedthrough of the input on the measurements, the two conditions can be merged to give rise to a necessary and sufficient condition.
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Dates et versions

hal-01918497 , version 1 (11-11-2018)

Identifiants

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Sebin Gracy, Federica Garin, Alain Kibangou. Input and State Observability of Network Systems with Time-Varying Topology. IEEE Transactions on Control of Network Systems, 2019, 6 (2), pp.897-905. ⟨10.1109/TCNS.2018.2880304⟩. ⟨hal-01918497⟩
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