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1

Global rational stabilization of a class of nonlinear time-delay systems

Echi Nadhem, Ghanmi Boulbaba

Archives of Control Sciences

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2019

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Vol. 29, No. 2

259--278

EN

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.

2

Robust controlled positive delayed systems with interval parameter uncertainties: A delay uniform decomposition approach

Elloumi W., Mehdi D., Chaabane M.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

441--450

EN

This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov–Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.

3

A periodic inventory control system with adaptive reference stock level for long supply delay

Chołodowicz E., Orłowski P.

Measurement Automation Monitoring

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2015

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Vol. 61, No. 12

568--572

EN

Modern inventory control is anchored in vastly advanced and complex models, which require considerable computational efforts. In this paper, we use a mathematical model of an inventory system with large supply delay and control system in order to optimize goods flow in inventory systems. The paper proposes the use of automatic control systems to control the system for supplementary orders. A discrete-time, dynamic model of the warehouse system is assumed for the analysis. For the given model, two automatic control systems: adaptive and classical non-adaptive periodic inventory systems , are analyzed. The non-adaptive control system is well known in the literature and the second one is its extension. The parameters of the control system are tuned by minimizing the cost function using a genetic algorithm for the assumed scenario for the market demand. Results of numerical simulations of the dynamical system and selected results in the objective space are presented in the paper.

4

On-line parameter and delay estimation of continuous-time dynamic systems

Kozłowski J., Kowalczuk Z.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

223--232

EN

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

5

Robust stability of positive linear time delay systems under time-varying perturbations

Ngoc P. H. A., Tinh C. T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 4

947--954

EN

By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.

6

Nonlinear adaptive time-delay control system

Halawa J.

Przegląd Elektrotechniczny

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2009

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R. 85, nr 3

28-29

EN

The paper puts forward a nonlinear adaptive time-delay control system with variable gain of PI or PID controller conditioned by amplitude of signal applied to the controllers section where its gain value is generated. Simulation studies for the exemplary time variable delay controlled system are also provided. In simulation tests the controlled system was approximated by simplified first-order model with variable delay.

PL

W pracy przedstawiono nieliniowy układ kontroli z z regulatorem typu PI i PID o zmiennym wzmocnieniu w zależności od wielkości błędu regulacji. Podano strukturę regulatora o adaptacyjnym wzmocnieniu. Badania symulacyjne przeprowadzono dla modelu obiektu pierwszego rzędu ze zmiennym opóźnieniem.

7

Robust Dynamic Input Reconstruction for Delay Systems

Kappel F., Maksimov V.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 2

283-307

EN

A problem of reconstruction of a non-observable control input for a system with a time delay is analyzed within the framework of the dynamical input reconstruction approach (see Kryazhimskii and Osipov, 1987; Osipov and Kryazhimskii, 1995; Osipov et al., 1991). In (Maksimov, 1987; 1988) methods of dynamical input reconstruction were described for delay systems with fully observable states. The present paper provides an input reconstruction algorithm for partially observable systems. The algorithm is robust to the observation perturbations.