Stability crossing surfaces for linear time-delay systems with three delays

Almodaresi, Elham; Bozorg, Mohammad

doi:10.1080/00207170903037739

Cited by 18 publications

(9 citation statements)

References 10 publications

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“…Among them are the linear matrix inequality (LMI) methods (Chen, Gu, & Nett, 1994;K. Gu, Kharitonov, & J.Chen, 2003;Nguyen, Ishihara, Krishnakumar, & Bakhtiari-Nejad, 2009) and the frequency based methods (Elham Almodaresi & Bozorg, 2009;Keqin Gu, Niculescu, & Chen, 2005;Sipahi & Olgac, 2005). The LMI methods compute conservative margins for delays, while the frequency based approaches are less flexible for more complicated cases of MIMO systems with uncertain models and external disturbances.…”

Section: Introductionmentioning

confidence: 98%

Stability domains of the delay and PID coefficients for general time-delay systems

Almodaresi

Bozorg

Taghirad

2015

International Journal of Control

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Time delays are encountered in many physical systems, and they usually threaten the stability and performance of closed-loop systems. The problem of determining all stabilizing PID controllers for systems with perturbed delays is less investigated in the literature. In this study, the Rekasius substitution is employed to transform the system parameters to a new space. Then, the singular frequency (SF) method is revised for the Rekasius transformed system (RTS). A novel technique is presented to compute the ranges of time delay for which stable PID controller exists. This stability range cannot be readily computed from the previous methods. Finally, it is shown that similar to the original SF method, finite numbers of singular frequencies are sufficient to compute the stable regions in the space of time delay and controller coefficients.

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Section: Introductionmentioning

confidence: 98%

Stability domains of the delay and PID coefficients for general time-delay systems

Almodaresi

Bozorg

Taghirad

2015

International Journal of Control

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“…This task becomes much more complex as the number of delays, p , increases [22]. For 3 ≥ p , only a limited number of reports exist in the literature ( [1], [16], [32], [33], [36]). First three deal with a similar subclass of MTDS excluding commensurate and cross-talking delay terms in the corresponding characteristic equation.…”

Section: Introductionmentioning

confidence: 99%

“…This is not allowed. As a consequence, the projection of space, i.e., the curve segment AB , either forms a closed loop with curve1 C or extends to infinity as curve2 C does inFig. 1.…”

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confidence: 99%

Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays

Gao

Olgaç

2016

Automatica

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The stability of linear time invariant (LTI) systems with independent multiple time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. It is known that for such systems, all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays [34]. They are called kernel hypersurfaces (KH). The complete description of KH is the only prerequisite for the CTCR stability assessment procedure. As the number of delays increases, however, their evaluation becomes infeasible. Instead, we present a procedure to extract the 2-D cross-sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays. In the 2-delay domain of interest, the exact upper and lower bounds of the imaginary spectra are determined. For this, a combination of half-angle tangent representation of the characteristic equation and the Dixon resultant theory is used as the main contributions of this paper. The complete KH are obtained by sweeping the root crossing frequency in this interval. Using this knowledge CTCR creates the cross-section of the stability map in the domain of the two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones.

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“…See Almodaresi and Bozorg [12] and Gu and Naghnaeian [13]. As already shown in Figure 2, a(iω) = 0 means that these three vectors in a(iω) must form a triangle having the dotted base with interior angles, θ 1 and θ 2 .…”

Section: Construction Of Stability Switching Curvesmentioning

confidence: 99%

A Heterogeneous Agent Model of Asset Price with Three Time Delays

Matsumoto

Szidarovszky

2016

Front. Appl. Math. Stat.

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This paper considers a continuous-time heterogeneous agent model of a financial market with one risky asset, two types of agents (i.e., the fundamentalists and the chartists), and three time delays. The chartist's demand is determined through a nonlinear function of the difference between the current price and a weighted moving average of the delayed prices whereas the fundamentalist's demand is governed by the difference between the current price and the fundamental value. The asset price dynamics is described by a nonlinear delay differential equation. Two main results are analytically and numerically shown:(i) a single delay destabilizes the market price and generates cyclic oscillations around the equilibrium; (i) under multiple delays, stability loss and gain repeatedly occur as the length of the delay increases.

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Stability crossing surfaces for linear time-delay systems with three delays

Cited by 18 publications

References 10 publications

Stability domains of the delay and PID coefficients for general time-delay systems

Stability domains of the delay and PID coefficients for general time-delay systems

Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays

A Heterogeneous Agent Model of Asset Price with Three Time Delays

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