A practical method for analyzing the stability of neutral type LTI-time delayed systems

Olgaç, Nejat; Sipahi, Rifat

doi:10.1016/j.automatica.2003.12.010

Cited by 101 publications

(96 citation statements)

References 13 publications

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“…The root tendency will be better explained in the sequel, but as in the nonfractional case [Olgac and Sipahi [2004]], it is constant with respect to any sequential crossings in (15).…”

Section: Crossing Positionmentioning

confidence: 99%

“…It is known that an interesting phenomenon, namely stability windows, might happen. There has been a large effort to deal with this problem, as can be seen by the large quantity of articles dealing with it for the standard case; see [Walton and Marshall [1987]], [Olgac and Sipahi [2004]], and many others. Recently, [Fioravanti et al [2010a]] brought another numerical technique to deal with this problem, and further extended its capabilities by using the results obtained to find the position of the unstable poles.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The root tendency will be better explained in the sequel, but as in the nonfractional case [Olgac and Sipahi [2004]], it is constant with respect to any sequential crossings in (15).…”

Section: Crossing Positionmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Inner-outer factorizations require finding C+ roots of a quasi-polynomial, for which several algorithms exist by now, see e.g. [5,12,17] and their references. Using these algorithms and the methods developed for the H∞ control of general infinite dimensional systems, (see e.g.…”

Section: Design Of C 1 Maximizing the Integral Action Gainmentioning

confidence: 99%

Integral Action Controllers for Systems with Time Delays

Özbay

Gündeş

2009

Topics in Time Delay Systems

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Summary. Consider a stabilizing controller C1 for a given plant P . If C1 and P do not have any zeros at the origin, then one can use a cascade connected PI (proportional plus integral) controller Cpi with C1 and keep the feedback system stable. In this work we examine the allowable range of the integral action gain in Cpi, and discuss how C1 should be chosen to maximize this range for systems with time delays.

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“…The computation of these parameters is complicated due to the infinite sensitivity of the characteristic roots, thus special methods have to be applied. For the stability computation of systems with free delay parameters the Cluster Treatment of Characteristic Roots (CTCR) method is an appropriate choice [Olgac and Sipahi (2004); Sipahi (2005); Sipahi and Olgac (2006); Olgac et al (2006Olgac et al ( , 2008; Sipahi et al (2010)] or algorithms presented in [Jarlebring (2007); Péics and Karsai (2002)] can be applied. In [Michiels et al (2009)] the delay dependency structure is also considered.…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation Method for Strong Stability Area of Neutral Equations

Bachrathy¹

2016

IFAC-PapersOnLine

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A reliable method for the computation of the strong stable area of neutral delay differential equations is presented. A special neutral system with commensurate delays is analysed. Phase parameters are used to determine all possible parameter points where a critical characteristic root may occur for a given time delay ratio. An extra condition is formulated to define the boundary curves of the robust stable area. The corresponding co-dimension 3 parameter problem in the 4 dimensional parameter space is solved efficiently by the MultiDimensional Bisection Method. Finally the so-called instability gradients are used to classify the distinct domains of the chart. It is shown, that the computational time of the proposed method to obtain the strong stable area is comparable to the CPU time needed for the computation of the stability chart for a given fixed delay ratio.

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A practical method for analyzing the stability of neutral type LTI-time delayed systems

Cited by 101 publications

References 13 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

Integral Action Controllers for Systems with Time Delays

Efficient Computation Method for Strong Stability Area of Neutral Equations

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