Paper Info
Title
Input and State Observability of Network Systems With Time-Varying Topology
Abstract
We aim to study the problem of reconstructing the initial state as well as the sequence of unknown inputs [input and state observability (ISO)] for linear network systems having time-varying topology. Evolution of such systems can be represented by a collection of graphs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \mathcal {G}_{k}\rbrace$</tex-math></inline-formula> . We find conditions under which the system with a pattern of fixed zeros imposed by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \mathcal {G}_{k}\rbrace$</tex-math></inline-formula> is ISO: 1) for almost all choices of edge weights in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \mathcal {G}_{k}\rbrace$</tex-math></inline-formula> (structural ISO) and 2) for all nonzero choices of edge weights in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \mathcal {G}_{k}\rbrace$</tex-math></inline-formula> (strongly structural ISO). We introduce two suitable descriptions of the whole collection of graphs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \mathcal {G}_{k}\rbrace$</tex-math></inline-formula> called the dynamic graph and dynamic bipartite graph. Two equivalent characterizations of structural ISO are then stated in terms of the existence of linking and matching of a 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 a 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.
Year
DOI
Venue
2019
10.1109/TCNS.2018.2880304
IEEE Transactions on Control of Network Systems
Keywords
Field
DocType
ISO,Topology,Network topology,Observability,Time-varying systems,ISO Standards,Control systems
Topology,Graph,Observability,Bipartite graph,Linear network,Feedthrough,Mathematics
Journal
Volume
Issue
ISSN
6
2
2325-5870
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Sebin Gracy100.68
Federica Garin25511.52
Alain Y. Kibangou39512.01