Observability of nonlinear systems

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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“…Step 0: Since θ Y = 2 and ϕ e (Y) = {x 1 , x 2 } we have that V * M 0 = Y = {y 1 , y 2 } satisfies condition (15). So, we deduce …”

Section: Algorithmmentioning

confidence: 93%

“…In fact, it results from [3,13,15,21,24] that a nonlinear system is observable if it can be found an input such that any pair of initial states are distinguishable by observation of the corresponding output. The distinguishability of two initial states is thus depending on the input applied to the system.…”

Section: Introductionmentioning

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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“…Other important observability results for general systems are given in [21], [36], [37]. Now we consider some specific classes of nonlinear processes.…”

Section: Lq(>)(x) =Ax (X)q(x)mentioning

confidence: 99%

Recent Developments and Future Perspectives in Nonlinear System Theory

Casti¹

1982

SIAM Rev.

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“…However, for nonlinear systems, the distinguishability of two initial states depends on the input applied to the system. In this respect, a BLS is observable if it can be found an input such that any pair of initial states are distinguishable by observation of the corresponding outputs (Williamson, 1977;Kou et al, 1996). From the latter definition, the notion of universal input is defined in (Gauthier and Bornard, 1981;Hermann and Krener, 1977) as an input for which every pair of initial states can be distinguished by observation of the corresponding outputs.…”

Section: Introductionmentioning

confidence: 99%

Generic uniform observability analysis for bilinear systems

Boukhobza

2008

Automatica

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In this paper, we study the property of generic uniform observability for structured bilinear systems. More precisely, to check whether or not a structured bilinear system generically uniformly observable, we provide a group of necessary conditions and second group of sufficient ones. These conditions are expressed in quite simple graphic-terms. On the one hand, all the given conditions are easy to check because they deal with finding paths in a digraph. On the other hand, the proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as it may be the case during a conception stage.

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Observability of nonlinear systems

Cited by 118 publications

References 2 publications

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

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

Recent Developments and Future Perspectives in Nonlinear System Theory

Generic uniform observability analysis for bilinear systems

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