An Operational Standpoint in Electrical Engineering

Rotella, Frédéric; Zambettakis, Irène

doi:10.7251/els1317071r

Cited by 3 publications

(5 citation statements)

References 42 publications

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“…Furthermore, the dynamic system described by equation [20], is asymptotically stable according to [21,22] when the Stodola stability condition is met and all major minors (subdeterminants) of the Hurwitz matrix Hi are positive:…”

Section: Methodsmentioning

confidence: 99%

“…The operator calculus is an alternative to the conventionally used Laplace transform. According to the sources [22], the author of this operator is Cauchy, and according to sources [23] is Kirchhoff. Rottella provided evidence based on rigorous consistency on the operator in 2013.…”

Section: Methodsmentioning

confidence: 99%

“…Thus, according to Rotella [22], the Cauchy derivative operator (operator calculus) m can be defined as…”

Section: Methodsmentioning

confidence: 99%

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Financial Stability Control for Business Sustainability: A Case Study from Food Production

Macak¹

2022

Mathematics

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Conventional financial management methods, based on extrapolation approaches to financial analysis, often reach their limits due to violations of stationary controlled financial variables, for example, interventions in the economy and social life necessary to manage the COVID-19 pandemic. Therefore, we have created a procedure for controlling financial quantities, which respects the non-stationarity of the controlled quantity using the maximum control deviation covering the confidence interval of a random variable or random vector. For this interval, we then determined the algebraic criteria of the transfer functions using the Laplace transform. For the Laplace transform, we determined the theorem on the values of the stable roots of the characteristic equation, including the deductive proof. This theorem is directly usable for determining the stability of the management for selected financial variables. For the practical application, we used the consistency of the stable roots of the characteristic equation with the Stodola and Hurwitz stability conditions. We demonstrated the procedure for selected quantities of financial management in food production. In conclusion, we proposed a control mechanism for the convergence of regulatory deviation using a combination of proportional and integration schemes. We also determined the diversification of action interventions (into development, production, and marketing) using a factorial design.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Financial Stability Control for Business Sustainability: A Case Study from Food Production

Macak¹

2022

Mathematics

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“…We consider a system modelized, after linearization around the set point [3,23], by the state model :…”

Section: Observation Of a State Linear Functionalmentioning

confidence: 99%

“…Among all the realization techniques for usual differential equations [14,23] the most appropriate one is based on factorization, after operational coding, of the differential equation (7). Using the Heaviside coding of the time derivative operator p, so the coding of the time integration operator p −1 as well, this differential equation can be written :…”

Section: Design Of a Luenberger Observermentioning

confidence: 99%

Some new standpoints in the design of asymptotic functional linear observers

Rotella

Zambettakis

2015

ESAIM: Proc.

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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.

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Initial Conditions in Time- and Frequency-Domain System Identification: Implications of the Shift Operator Versus the Z and Discrete Fourier Transforms

2018

IEEE Control Syst.

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An Operational Standpoint in Electrical Engineering

Cited by 3 publications

References 42 publications

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Some new standpoints in the design of asymptotic functional linear observers

Initial Conditions in Time- and Frequency-Domain System Identification: Implications of the Shift Operator Versus the Z and Discrete Fourier Transforms

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