Observability analysis by Poincaré normal forms

International audienceThis paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the effect of the normal quadratic numbers on the observer design is pointed out. Finally, a faster observability analysis is proposed using characteristic matrices and normal quadratic numbers. Throughout the paper, academic examples as well as bio-reactor example highlight our purpose

A triangular canonical form for a class of 0-flat nonlinear systems

International audienceThis article proposes a triangular canonical form for a class of 0-flat nonlinear systems. Necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0-flat canonical form, which enables us to compute the flat output as well

A nonlinear canonical form for reduced order observer design

International audienceThis paper presents a nonlinear canonical form which is used for the design of a reduced order observer. Sufficient and necessary geometric conditions are given in order to transform a special class of nonlinear systems to the proposed nonlinear canonical form and the corresponding reduced order observer is analyzed

Single output dependent quadratic observability normal form

International audienceIn this paper, two quadratic observability normal forms dependent on output respectively correspondent to drift dominant term and forced dominant term are firstly discussed. Moreover characteristic numbers are studied in order to simplify the calculation of these two normal forms

Single Output Dependent Observability Normal Form

International audienceThis paper gives the sufficient and necessary conditions which guarantee the existence of a diffeomorphism in order to transform a nonlinear system without inputs into a canonical normal form depending on its output. Moreover we extend our results to a class of systems with inputs

Geometrical Conditions for Output Depending Observability Normal Form

International audienceWe give geometrical conditions, which guarantee the existence of a diffeomorphism in order to transform a nonlinear system without inputs into a canonical normal form depending on its output. Moreover we extend our results to a class of systems with inputs. We end this paper by some examples and its simulations to highlight the proposed algorithm

Multi-Output Dependent Observability Normal Form

International audienceThis article gives the sufficient condition which guarantees the existence of a reference frame in which a multi-output nonlinear system is linearizable with a linear part depending on its outputs. Our method is based on the design of a reference frame associated with nonlinear observable systems. Moreover, we give the generalization of the result obtained in [5] and [19]. And some examples are given in order to highlight our thinking

Quelques commentaires sur la linéarisation de l'erreur de l'observation multi-sorties

International audienceCe papier donne quelques idées et commentaires sur les conditions géométriques qui permettent de dire si un système non linéaire multi sorties possède, à un changement de coordonnées près, une erreur d'observation linéaire. Plus précisément, nous allons concentrer notre point de vu sur les travaux de Krener et Respondek d'une part et ceux de Xia et Gao d'autre part. Nous allons aussi commenter le "soit disant" contre exemple de Xia et Gao. Puis, nous allons présenter l'algorithme de la linéarisation de l'erreur de l'observation par extension dynamique

Observability forms for switched systems with Zeno phenomenon or high switching frequency

International audienceThis paper deals with the observability of a class of switched systems with Zeno phenomenon or high switching frequency. Particularly, three observability forms are proposed and the observability for each form with knowledge of filtered switching signal is analyzed. Meanwhile, sufficient and necessary conditions for the existence of a diffeomorphism to transform a class of switched systems into one of such forms are presented. Examples and simulations are given at the end to highlight the theoretical results

Observability Normal Forms for a class of switched systems with zeno phenomena

International audienceThis paper deals with necessary and sufficient conditions to transform a class of switched systems to a particular form dedicated to observer design with and without zeno phenomena. Meanwhile, sufficient observability conditions for switched system with or without zeno phenomena are given. In the last section, some observer structures are proposed upon two academical examples