Minimal single linear functional observers for linear systems

Rotella, Frédéric; Zambettakis, Irène

doi:10.1016/j.automatica.2010.10.027

Cited by 47 publications

(33 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can be concluded that Conditions III and IV together are the necessary and sufficient conditions for the existence of an asymptotic UIFO with structure (2), and of order l for the system (14). Moreover, for the aim of the present paper, which is designing a proper UIFO, it can be shown that Conditions IV and II are identical.…”

Section: Remark 10mentioning

confidence: 73%

See 1 more Smart Citation

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Mohajerpoor

Asayesh

Nahavandi

2015

Journal of Process Control

View full text Add to dashboard Cite

Section: Remark 10mentioning

confidence: 73%

“…Functional observers are a generalized version of ordinary fullorder or reduced-order Luenberger observers that are aimed at reconstructing a single or multiple functions of the states of the system [12][13][14][15]. This class of estimators has superiority in giving observers with lower order than the ordinary reduced-order observers.…”

Section: Introductionmentioning

confidence: 99%

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Mohajerpoor

Asayesh

Nahavandi

2015

Journal of Process Control

View full text Add to dashboard Cite

“…This approach has allowed to propose stable Luenberger observers with minimal order to estimate a linear form of the state in [24]. It has been shown there that increasing index ν in the fundamental relation (5) allows to design a stable observer for which more and more poles can be fixed.…”

Section: Single Linear Functional Observermentioning

confidence: 99%

Some new standpoints in the design of asymptotic functional linear observers

Rotella

Zambettakis

2015

ESAIM: Proc.

View full text Add to dashboard Cite

Abstract. The owl of Minerva spreads its wing only with the falling of the dusk. The aim of this work is to provide some new trends in the observation for linear systems. In the general framework of designing linear functional observers for linear systems the necessary and sufficient existence conditions are well known. Whether in the O'Reilly textbook or in the recently published ones on this topic, and, roughly speaking, the design methods can be categorized in two kinds. The first one is based on the solution of a Sylvester equation and a projection of the observed linear functional. The second one, based on the recent notion of functional observability, starts from the Darouach criterion which is an Popov-Belevitch-Hautus type one. Nevertheless, the main drawback of the deduced methods is that they cannot be used for linear time-varying systems. These models are of primary importance, for instance with linearization about a trajectory. Consequently, we cope with this problem by considering a new point of view for the design of linear functional observers. We see also that Darouach observers or Cumming-Gopinath observers are particular cases of the proposed methodology. For simplicity sake we suppose the system has no unknown inputs and is not described by a distributed parameters model as well. Nevertheless, these cases can be thought as possible extensions of the presented standpoints.Résumé. La chouette de la connaissance ne vole qu'à la nuit tombée. L'objet de cet article est de proposer des pistes pour l'observation dans le cadre des systèmes linéaires. De façon plus générale, en considérant l'observation de fonctions linéaires de l'état d'un modèle linéaire, les conditions nécessaires et suffisantes d'existence de ces observateurs sont connues depuis longtemps. Que ce soit dans l'ouvrage de base de O'Reilly ou dans les ouvrages plus récents qui traitent de ce sujet, les différentes méthodes de conception d'un observateur de fonctionnelle linéaire peuvent, schématiquement,être rassemblées en deux groupes. Celles qui demandent la résolution d'uneéquation de Sylvester et d'uneéquation de projection et celles basées sur l'extension du critère d'existence de Darouach, ces dernières utilisant un critère de type Popov-Belevitch-Hautus. Ainsi les méthodes déduites de ces critères peuventêtre difficilementétendues aux systèmes linéaires non stationnaires. De façonà contourner cet inconvénient majeur lorsque l'on songeà la linéarisation autour d'une trajectoire, nous proposons une technique pratique et systématique de conception d'un observateur. On montre par exemple que les observateurs de Darouach ou de Cumming-Gopinath n'en sont que des cas particuliers. Bien sûr, pour ne pas compliquer inutilement la présentation nous n'envisagerons que des modèles linéaires stationnaires de dimension finieà entrées toutes connues, les autre situations pouvantêtre envisagéesà titre d'extension.

show abstract

“…However, those conditions are for the minimum order functional observer, i.e the order equal to the number of functions to be estimated. In many cases when these conditions are not satisfied, it is still possible to increase the order of the observer in order to design a stable functional observer for the system ( [20], [21], [22]). For such cases, two interesting questions would be as follows: 1) when is it possible to design a functional observer by increasing its order, and 2) how to design a functional observer with the minimum possible order.…”

Section: Introductionmentioning

confidence: 99%

On unknown-Input Functional Observability of linear systems

Mohajerpoor

Asayesh

Nahavandi

2015

2015 American Control Conference (ACC)

View full text Add to dashboard Cite

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced, and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.Keywords: Unknown-input functional observers, functional observability, invariant zeros and transmission zeros, null space and range space

show abstract

Minimal single linear functional observers for linear systems

Cited by 47 publications

References 23 publications

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Some new standpoints in the design of asymptotic functional linear observers

On unknown-Input Functional Observability of linear systems

Contact Info

Product

Resources

About