Stability Crossing Curves of Shifted Gamma-Distributed Delay Systems

Morărescu, Irinel-Constantin; Niculescu, Silviu–Iulian; Gu, Keqin

doi:10.1137/060670766

Cited by 42 publications

(45 citation statements)

References 9 publications

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“…Gathering the former relations (12), (13), it is straightforward to prove that separator (19) along with (18) satisfies inequality (4), which concludes the proof.…”

Section: Resultsmentioning

confidence: 77%

“…. , Q r ∈ R 2n×2n and R ∈ R n×n , then system (2) is asymptotically stable for the given h, if the LMI condition (3) holds with Θ, E and A defined as (19) and (22).…”

Section: Resultsmentioning

confidence: 99%

“…and Θ, E, A(h) defined as (19) and (27),(29), then system (2) is asymptotically stable for h, such that h min ≤ h ≤ h max .…”

Section: Proof 6 Omittedmentioning

confidence: 99%

“…Nevertheless, establishing structural properties such as stability in the presence of the distributed kernel are much more difficult than the pointwise delay case. One first possibility is to use frequency approaches like [19] or [2] but these techniques are restricted to nominal systems without uncertainties. Another popular way to establish robust stability tests remains the use of adapted Lyapunov-Krasosvkii functional.…”

Section: Introductionmentioning

confidence: 99%

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Delay Range Stability of distributed time delay systems

Gouaisbaut

Ariba

2009

IFAC Proceedings Volumes

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This paper is dedicated to the stability analysis of a class of uncertain distributed delay systems. We focus to the case where the kernel can be modelled as a polynomial function. The results are constructed by rewriting the system as an uncertain interconnected model and appropriate robust control tools as quadratic separation are then used to address to stability issue. Furthermore, some relations that highlight features of the delayed term are added to the interconnected model leading then to the conservatism reduction. At last, stability conditions are expressed in terms of LMIs which can be solved efficiently. Finally, some numerical examples show the effectiveness the proposed method.

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“…Gathering the former relations (12), (13), it is straightforward to prove that separator (19) along with (18) satisfies inequality (4), which concludes the proof.…”

Section: Resultsmentioning

confidence: 77%

“…. , Q r ∈ R 2n×2n and R ∈ R n×n , then system (2) is asymptotically stable for the given h, if the LMI condition (3) holds with Θ, E and A defined as (19) and (22).…”

Section: Resultsmentioning

confidence: 99%

“…and Θ, E, A(h) defined as (19) and (27),(29), then system (2) is asymptotically stable for h, such that h min ≤ h ≤ h max .…”

Section: Proof 6 Omittedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delay Range Stability of distributed time delay systems

Gouaisbaut

Ariba

2009

IFAC Proceedings Volumes

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“…Note that g(ξ) ≥ 0 for all ξ ≥ 0 and ∞ 0 g(ξ)dξ = 1. A motivation for the consideration of this type of delay distribution can be found in [6].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of coupled nonlinear oscillators with shifted gamma-distributed delays

Morărescu

Michiels

Jungers

2013

2013 American Control Conference

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Abstract-We derive conditions for the synchronization of coupled nonlinear oscillators affected by distributed delays in the interconnections. The distributed delays are characterized by a gamma-distribution kernel with a gap. The approach is based on the stability analysis of synchronized equilibria in the (delays,gain) parameter space and the characterization of the structure of the emanating solutions at the bifurcations. The results are applied to networks of coupled Lorenz system. In particular it is shown that, independently of the network topology, for sufficiently large coupling gains the distribution of the delay has a stabilizing effect on the stability of the synchronized equilibrium.

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Effect of a distributed delay on relative stability of diffusely coupled systems, with application to synchronized equilibria

Morărescu

Michiels

Jungers

2015

Int. J. Robust. Nonlinear Control

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SUMMARYWe perform a linear stability analysis of synchronized equilibria in networks of diffusely coupled oscillators, affected by distributed delays in the coupling, and we characterize the structure of the emanating solutions in the bifurcations, under the assumption that the delay kernels are equal to each other. The motivation comes from the fact that valuable quantitative and qualitative information about the occurrence and type of synchronous or partially synchronous solutions can be obtained from this linear analysis. We analyze stability of synchronized equilibria as a function of the parameters of a so-called shifted gamma-distributed delay, which allows to represent or approximate a large class of distributed delay kernels. We also present an asymptotic analysis method, which is particularly suitable for studying the effect of a distribution of delays on stability. We apply the methods to networks of coupled Lorenz systems, where we highlight that stability is favored by a distributed delay compared with a discrete delay with the same average value. Among others, we show that if the coupling is diffusive, the synchronized equilibria become asymptotically stable for large values of the coupling gain, that is, the systems locally asymptotically synchronize at an equilibrium, independently of the network topology.

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Stability Crossing Curves of Shifted Gamma-Distributed Delay Systems

Cited by 42 publications

References 9 publications

Delay Range Stability of distributed time delay systems

Delay Range Stability of distributed time delay systems

Synchronization of coupled nonlinear oscillators with shifted gamma-distributed delays

Effect of a distributed delay on relative stability of diffusely coupled systems, with application to synchronized equilibria

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