A graph-theoretic characterization for the rank of the transfer matrix of a structured system

Woude, Jacob van der

doi:10.1007/bf02551379

Cited by 78 publications

(54 citation statements)

References 4 publications

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“…These conditions are generic, in the sense that they hold for almost all numerical systems with the same structure, and they can be efficiently verified. As a complementary result, we extend a result of [27] on structural left-invertibility to regular descriptor systems. Finally, with respect to our earlier work [20], [21], we consider continuous-time descriptor systems, and we include parameters constraints.…”

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confidence: 72%

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Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,862

1,166

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Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial process control and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper (i) we propose a mathematical framework for cyberphysical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (iii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

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confidence: 72%

“…) be the tuple of structure matrices associated with the system (1) [27]. We associate a directed input/state/output graph G iso = (V, E)…”

Section: B Graph-theoretic Monitoring Limitationsmentioning

confidence: 99%

Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,862

1,166

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“…, y i k T . Let us denote byC λ the matrix such thatỹ =C λ x, then from the results on the matrices generic rank [18,23],…”

Section: Resultsmentioning

confidence: 99%

“…This property can be directly deduced from the results of [23] or from the results related to the maximum matching notion [17].…”

Section: Resultsmentioning

confidence: 99%

Uniform Observability Analysis for Structured Bilinear Systems A Graph-theoretic Approach

Boukhobza¹,

Hamelin²,

Sauter³

2006

European Journal of Control

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To cite this version:Taha Boukhobza, Frédéric Hamelin, Dominique Sauter. Uniform observability analysis for structured bilinear systems: A graph-theoretic approach. European Journal of Control, Lavoisier, 2006, 12 (5) Abstract This paper deals with the analysis of generic uniform observability for structured bilinear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. We express, in graphical terms two conditions, the first one is necessary and the second one is sufficient, to check whether or not they are generically uniformly observable. These conditions are quite easy to verify because they are based on comparisons of integers and on finding edges and subgraphs in a digraph. Therefore, our approach is very well suited to study large scale and/or uncertain systems.

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“…Theorem 3 ([21], [22]): Let the graph of a structured linear system be given by H. Then the generic normal rank of the transfer function of the system is equal to the maximal size of a linking in H from I to O.…”

Section: B Structured Systemsmentioning

confidence: 99%

The wireless control network: Monitoring for malicious behavior

Sundaram

Pajić

Hadjicostis

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

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We consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. In a companion paper, we developed a protocol where each node repeatedly transmits a linear combination of the values in its neighborhood. For certain topologies, we showed that these linear combinations can be designed so that the closed loop system is stable (i.e., the wireless network itself acts as a controller for the plant). In this paper, we design a Intrusion Detection System (IDS) for this control scheme, which observes the transmissions of certain nodes in the network and uses that information to (a) recover the plant outputs (for data-logging and diagnostic purposes) and (b) identify malicious behavior by any of the wireless nodes in the network. We show that if the connectivity of the network is sufficiently high, the IDS only needs to observe a subset of the nodes in the network in order to achieve this objective. Our approach provides a characterization of the set of nodes that should be observed, a systematic procedure for the IDS to use to identify the malicious nodes and recover the outputs of the plant, and an upper bound on the delay required to obtain the necessary information. Abstract-We consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. In a companion paper, we developed a protocol where each node repeatedly transmits a linear combination of the values in its neighborhood. For certain topologies, we showed that these linear combinations can be designed so that the closed loop system is stable (i.e., the wireless network itself acts as a controller for the plant). In this paper, we design a Intrusion Detection System (IDS) for this control scheme, which observes the transmissions of certain nodes in the network and uses that information to (a) recover the plant outputs (for data-logging and diagnostic purposes) and (b) identify malicious behavior by any of the wireless nodes in the network. We show that if the connectivity of the network is sufficiently high, the IDS only needs to observe a subset of the nodes in the network in order to achieve this objective. Our approach provides a characterization of the set of nodes that should be observed, a systematic procedure for the IDS to use to identify the malicious nodes and recover the outputs of the plant, and an upper bound on the delay required to obtain the necessary information.

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A graph-theoretic characterization for the rank of the transfer matrix of a structured system

Cited by 78 publications

References 4 publications

Attack Detection and Identification in Cyber-Physical Systems

Attack Detection and Identification in Cyber-Physical Systems

Uniform Observability Analysis for Structured Bilinear Systems A Graph-theoretic Approach

The wireless control network: Monitoring for malicious behavior

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