Analysis of fractional delay systems of retarded and neutral type

Bonnet, Catherine; Partington, Jonathan R.

doi:10.1016/s0005-1098(01)00306-5

Cited by 169 publications

(111 citation statements)

References 6 publications

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“…The BIBO-stability (finite L ∞ -gain) of fractional systems with delays has been considered in [Bonnet and Partington [2002]] where it is shown that BIBO stability conditions already known for delay systems can be extended to the case of fractional delay systems. As BIBO-stability implies H ∞ -stability (see [Mäkilä and Partington [1993], Partington and Mäkilä [1994]]), similar results can be derived immediately for H ∞ -stability.…”

Section: Stability Of Fractional-order Systems With Delaymentioning

confidence: 99%

Stability windows and unstable root-loci for linear fractional time-delay systems

Fioravanti

Bonnet

Özbay

et al. 2011

IFAC Proceedings Volumes

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The main point of this paper is on the formulation of a numerical algorithm to find the location of all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by the asymptotic position of the chains of poles and conditions for their stability, for a small delay. When these conditions are met, we continue by means of the root continuity argument, and using a simple substitution, we can find all the locations where roots cross the imaginary axis. We can extend the method to provide the location of all unstable poles as a function of the delay. Before concluding, some examples are presented.

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Section: Stability Of Fractional-order Systems With Delaymentioning

confidence: 99%

Stability windows and unstable root-loci for linear fractional time-delay systems

Fioravanti

Bonnet

Özbay

et al. 2011

IFAC Proceedings Volumes

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“…Note that the zeros of characteristic equation (1) are in fact the poles of the system under investigation. We find out from [6] that the transfer function of a system with a characteristic equation in the form of (1) will be H ∞ stable if, and only if, it doesn't have any pole at ℜ(s) ≥ 0. For fractional order systems, if a auxiliary variable of v = α √ s is used, a practical test for the evaluation of stability can be obtained.…”

Section: Preliminaries and Defintionsmentioning

confidence: 99%

“…In [6], the necessary and sufficient conditions for the BIBO stability of fractional order delay systems have been introduced. From the numerical analysis point of view, the effective numerical algorithms have been discussed in [7] and [8] for the evaluation of BIBO stability of fractional order delay systems.…”

Section: Introductionmentioning

confidence: 99%

Direct Method for Stability Analysis of Fractional Delay Systems

Pakzad

Nekui

2013

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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In this paper, a direct method is presented to analyze the stability of fractional order systems with single and multiple commensurate time delays. Using the approach presented in this study, first, without using any approximation, the transcendental characteristic equation is converted to an algebraic one with some specific crossing points. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Finally, the concept of stability is expressed as a function of delay. An illustrative example is presented to confirm the proposed method results.

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“…Given all the parameters of plant (1), our goal is to design a classical Proportional + Integral + Differential (PID) controller in the form [32] that H ∞ -stability of these systems is equivalent to their BIBO-stability, a necessary and sufficient condition being that the system has no poles in the right half-plane (including no pole of fractional order at s = 0) and a numerical algorithm to test this property is available in [33]. In the case of fractional systems of commensurate order, checking stability can be done as follows (see e.g.…”

Section: Problem Definitionmentioning

confidence: 99%

PID controller design for fractional-order systems with time delays

Özbay

Bonnet

Fioravanti

2012

Systems & Control Letters

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a b s t r a c tClassical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of s α , where 0 < α < 1, and s is the Laplace transform variable. Effect of input-output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.

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Analysis of fractional delay systems of retarded and neutral type

Cited by 169 publications

References 6 publications

Stability windows and unstable root-loci for linear fractional time-delay systems

Stability windows and unstable root-loci for linear fractional time-delay systems

Direct Method for Stability Analysis of Fractional Delay Systems

PID controller design for fractional-order systems with time delays

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