Robust stability analysis of fractional order interval polynomials

Tan, Nusret; Özgüven, Ömerül Faruk; Özyetkin, M. Mine

doi:10.1016/j.isatra.2009.01.002

Cited by 131 publications

(120 citation statements)

References 29 publications

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“…Stability is fundamental to all control systems, certainly including fractional order control systems [1], [2], [3], [5], [7], [8], [9], [15], [16], [26], [27], [29], [30]. There have been some stability results about the fractional-order systems with interval uncertainties [1], [2], [5], [29].…”

Section: Introductionmentioning

confidence: 99%

“…There have been some stability results about the fractional-order systems with interval uncertainties [1], [2], [5], [29]. For example, for FO-LTI interval systems described in the transfer function form, the stability issue was discussed in [29].…”

Section: Introductionmentioning

confidence: 99%

“…For example, for FO-LTI interval systems described in the transfer function form, the stability issue was discussed in [29]. Note that, in [29], the results were only for single-input single-output FO-LTI systems. For FO-LTI interval systems described in the state-space form, the robust stability problem was firstly solved in [5], where the matrix perturbation theory was used to find the ranges of the corresponding interval eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

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Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Chen

2013

fcaa

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This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.MSC 2010 : Primary 26A33; Secondary 34A08, 34D10, 93C73, 93D09, 93D21

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Chen

2013

fcaa

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“…En este sentido se ha intentado aplicar diferentes técnicas para la sintonización de controles fraccionales, como el método ZieglerNichols [40][41], series de polinomios [42], algoritmos genéticos [43], enjambres de partículas [44], teoría electromagnética [45], cuantificadores dinámicos [46] y modos deslizantes [47] [48]. Sin embargo, muchas de las técnicas usadas presentan problemas por la cantidad de parámetros que se requiere calcular, lo que se traduce en alta carga computacional y altos tiempos de procesamiento, siendo esta la razón de que muchos trabajos de implementación del control fraccional se hayan hecho sobre variables o procesos de reacción lenta, tales como el control de temperatura.…”

Section: Introductionunclassified

Control PID tipo fraccional para la posición del cabezal de una unidad de CD para aplicaciones en microscopia óptica

Valencia¹,

Cardona²

2012

Iteckne

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Resumen-En este artículo se diseña un control PID tipo fraccional para la posición del cabezal de una unidad de CD que se piensa emplear en el desarrollo de un microscopio óptico motorizado. En dicha aplicación se reemplazará el disco o CD por una placa con la muestra que va a ser estudiada, y se usará el cabezal de la unidad para iluminar la muestra. Con el controlador diseñado se busca que no haya dependencia del subcó-digo escrito en un CD para determinar la posición del cabezal, para lo cual se usará un ratón de computador como sensor de posición. También se busca un control que mejore el desempeño del sistema y que sea robusto frente a las incertidumbres en el modelo de la planta, razón por la cual se empleará un control tipo fraccional (PI^λD^μ) y se ajustarán los parámetros K_p, K_i, K_d, λ, μ con cinco especificaciones de robustez. Para la sintonización del control se utiliza la toolbox de optimización de Matlab con la función fmincon. Al final del artículo se presentan los resultados en simulación, se concluye sobre la resolución obtenida, la robustez del controlador y la viabilidad del sistema de control para ser empleado en un microscopio.Palabras clave-Control de posición, Control Fraccional, Control Robusto, Microscopía óptica, ratón óptico, unidad de CD.Abstract-On this work a fractional PID controller is designed for a CD pickup head position control that is intended to use in the development of a motorized optical microscope. In such an application the disk or CD would be replaced by a plate with the sample to be studied, and the pickup head would be used to illuminate the sample. The controller is designed in such a way that there is no dependence on a CD written subcode to determine the position of the head, and for this, a computer mouse is used as a position sensor. We also look for the controller to improve the system performance and to be robust against model uncertainties of the plant, that is why we use a fractional controller PI^λ D^μ and adjust the parameters K_p, K_i, K_dλ and μ according to five robustness rules. For tuning the control we use the Matlab optimization toolbox together with fmincon function. At the end of the paper we present the simulation results, concluding about the resolution obtained, the robustness of the controller and the viability of the control system to be used in a microscope.

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“…The problems of stability and robust stability of the standard fractional order linear systems have been investigated in [10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Robust stability of positive discrete-time linear systems of fractional order

Busłowicz¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order -in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order -in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order -in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

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Robust stability analysis of fractional order interval polynomials

Cited by 131 publications

References 29 publications

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Control PID tipo fraccional para la posición del cabezal de una unidad de CD para aplicaciones en microscopia óptica

Robust stability of positive discrete-time linear systems of fractional order

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