Complete stability robustness of third-order LTI multiple time-delay systems

Sipahi, Rifat; Olgaç, Nejat

doi:10.1016/j.automatica.2005.03.022

Cited by 173 publications

(143 citation statements)

References 9 publications

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“…Finally, with the help of these curves and developing sensitivity analysis, we can determine the parameter space that renders equation (3.3) asymptotically stable. The analysis requires explicit computation of the crossing directions on the stability crossing curves (Gu et al 2005;Sipahi & Olgac 2005), which may be towards either C + or C − , for the critical roots located on the imaginary axis and subject to variations with respect to the corresponding set of parameters. It is worth mentioning that the particular structure of the problem we are dealing with suggests treating the gain parameter and the delay parameter spaces independently, and to compute the stability crossing curves in each case.…”

Section: Stability Analysismentioning

confidence: 99%

Stability of car following with human memory effects and automatic headway compensation

Sipahi

Niculescu

2010

Phil. Trans. R. Soc. A.

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This paper addresses the study of some appropriate control strategies in order to guarantee the exponential stability of a class of deterministic microscopic car-following models including human drivers' memory effects and automated headway controllers. More precisely, the delayed action/decision of human drivers is represented using distributed delays with a gap and the considered automated controller is of proportional derivative type. The analysis is performed in both delay parameter and controller gain parameter spaces, and appropriate algorithms are proposed. Surprisingly, large delays and/or gains improve stability for the corresponding closed-loop schemes. Finally, some illustrative examples as well as various interpretations of the results complete the presentation.

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Section: Stability Analysismentioning

confidence: 99%

Stability of car following with human memory effects and automatic headway compensation

Sipahi

Niculescu

2010

Phil. Trans. R. Soc. A.

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“…There is however, very limited control synthesis studies in the literature on time delayed systems, again mainly due to the notoriety of the problem (Niculescu 2001;Filipovic and Olgac 2002;Insperger and Stépán 2005). Author's group has contributed in this field, both from the stability analysis and the control synthesis aspects of the research (Olgac and Sipahi 2002;Olgac, Ergenc and Sipahi 2005;Sipahi and Olgac 2005;Olgac and Sipahi 2006; * Author was affiliated with University of Connecticut when the work was done. Ergenc, Olgac and Fazelinia, 2007).…”

Section: Introductionmentioning

confidence: 99%

“…(Olgac and Sipahi 2002;Olgac and Sipahi 2004;Sipahi and Olgac 2005;Olgac and Sipahi 2006; as well as the strategies for stabilizing (or disturbance rejecting) control (Olgac, Ergenc and Sipahi 2005). …”

Section: Introductionmentioning

confidence: 99%

Inverting Control, a New Strategy on Time Delayed Systems

Ergenç

Fazelinia

Olgaç

2008

IFAC Proceedings Volumes

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In this paper we introduce a new control strategy for linear time invariant (LTI) systems with a single time delay. The delay appears within the feedback control logic. Earlier research on this class of systems determines the delay intervals for stable operations, exhaustively, exactly and completely. The newly developed inverting control logic suggests a very practical procedure of reversing the sign of the feedback control gain, in order to enlarge the stable delay intervals. This gives some additional capabilities to control system designer. The sign inversion idea is based on a critical mathematical feature of LTI-TDS (Time Delay Systems) which was first recognized under a paradigm called the Cluster Treatment of Characteristic Roots (CTCR). Several example case studies demonstrate the practicality and the advantages of the new control law.

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“…However, linear time-delay systems with multiple delays have not been much studied Shaked 2002, 2003;Gu 1997, Kolmanovskii andRichard 1999;Lewis and Anderson 1980;Sipahi and Olgac 2005;Vyhlidal and Zitek 2006;Suh and Bien 1982;Xu 1995). Lewis and Anderson (1980) and Suh and Bien (1982) developed some delay-independent stability criteria for linear time-delay systems with multiple delays using the technique of quasi-diagonal dominance.…”

Section: Introductionmentioning

confidence: 99%

“…Shaked (2002, 2003) introduced a descriptor model transformation method and suggested delay-dependent stability criteria for a linear time-delay system with multiple delays. Sipahi and Olgac (2005) proposed a unique procedure for a complete stability robustness of the third-order linear time delay systems with two delays. Vyhlidal and Zitek (2006) introduced two algorithms which provide the approximate (not exact) positions of the quasipolynomial roots located inside a selected region D.…”

Section: Introductionmentioning

confidence: 99%

On stability of linear time-delay systems with multiple delays

Park

Choi

Lim

2008

International Journal of Systems Science

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In this article, delay-dependent stability criteria for linear retarded and neutral systems with multiple delays are proposed by employing the Lyapunov-Krasovskii functional approach and integral inequality. By the N-segmentation of delay length, we obtain more relaxed results on the delay bounds which guarantee the asymptotic stability of the linear retarded and neutral systems with multiple delays. Simulation results show that the stability boundary calculated by the proposed stability criteria are very near to the real stability boundary of the example systems. Moreover, it is shown that the proposed stability criteria are less conservative than several other existing criteria.

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Complete stability robustness of third-order LTI multiple time-delay systems

Cited by 173 publications

References 9 publications

Stability of car following with human memory effects and automatic headway compensation

Stability of car following with human memory effects and automatic headway compensation

Inverting Control, a New Strategy on Time Delayed Systems

On stability of linear time-delay systems with multiple delays

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