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Input and State Observability of Linear Network Systems with Application to Security of Cyber Physical Systems


Directeur de thèse :     Alain KIBANGOU

Co-encadrant :     Federica GARIN

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (eeats)

Spécialité : Automatique et productique

Structure de rattachement : Grenoble-INP

Établissement d'origine :

Financement(s) : Contrat doctoral ; Sans financement


Date d'entrée en thèse : 01/10/2015

Date de soutenance : 23/11/2018


Composition du jury :
Sophie ACHARD, Examinatrice, Directrice de recherche, CNRS
Taha BOUKHOBZA, Rapporteur, Professeur, Université de Lorraine
Julien M. HENDRICKX, Rapporteur, Professeur, Ecole Polytechnique de Louvain
Giuseppe NOTARSTEFANO, Examinateur, Professeur, Université de Bologne
Alain KIBANGOU, Directeur de thèse, Maître de conférences, HDR, Univ. Grenoble Alpes
Federica GARIN, Encadrante de thèse, Chargée de recherche, Inria
Christian COMMAULT, Invité, Professeur émérite, Grenoble-INP


Résumé : This thesis deals with the notion of Input and State Observability (ISO) in linear network systems. One seeks graphical characterizations using the notion of structural (resp. s-structural) ISO. We first focus on linear time-invariant network systems, represented by fixed graphs, and provide characterizations for strong structural ISO. Thereafter, we turn our attention to linear time-varying network systems wherein we first narrow our attention to the particular case of fixed graphs (i.e., the structure of the graph remains fixed; the weights along the edges are allowed to vary, thereby giving rise to time-varying dynamics). We show that, under suitable assumptions on the structure of input, output and feedthrough matrices, ISO of a system is equivalent to observability of a suitably defined subsystem. Subsequently, we exploit this equivalence to obtain graphical characterizations of structural (resp. s-structural) ISO. Thereafter, for the LTV setting, we consider the more general case of time-varying graphs and furthermore make no assumptions on the structure of system matrices. We introduce two suitable descriptions of the whole collection of graphs, which are 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. Finally, we present an unbiased recursive algorithm that simultaneously estimates states and inputs. We focus on delay-L left invertible systems with intrinsic delay L greater than or equal to 1, where the input reconstruction is possible only by using outputs up to L time steps later in the future. By showing an equivalence with a descriptor system, we state conditions under which the timevarying filter converges to a stationary stable filter, involving the solution of a discrete-time algebraic Riccati equation.

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