A multistage reduction technique for feedback stabilizing distributed time-lag systems

Fiagbedzi, Yawvi A.; Pearson, A. E.

doi:10.1016/0005-1098(87)90005-7

Cited by 84 publications

(41 citation statements)

References 9 publications

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“…in the modeling of combustion chambers rocket motor with pressure feeding [4], [20]. Because of the significance of systems with distributed time-delay, as the controllers are usually digitally implemented, a growing attention has been devoted to studying distributed delay systems in recent years.…”

Section: Introductionmentioning

confidence: 99%

LMI based control design for linear systems with distributed time delays

Filasová¹,

Gontkovic²,

Krokavec³

2012

Archives of Control Sciences

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The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.

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Section: Introductionmentioning

confidence: 99%

LMI based control design for linear systems with distributed time delays

Filasová¹,

Gontkovic²,

Krokavec³

2012

Archives of Control Sciences

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“…Practical issues of such models are numerous in the literature. Distributed delay systems are often use to model the time lag phenomenon in thermodynamics (dynamics of combustion chambers in a liquid mono propellant rocket motor with pressure feeding, [5]), in ecology, epidemiology (predator-prey systems [8]). In all these cases, compared to a pointwise delay system, the use of a distributed kernel allows a thinner modelling of the interactions between the different system components.…”

Section: Introductionmentioning

confidence: 99%

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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“…As such, the unboundedness and the mode-dependence of such a distributed time-delay would have a great impact on the stability analysis on the overall coupled system. For the practical applications of such unbounded distributed delays, we refer the authors to [10], [11], [21]. It is worth mentioning that the finite distributed delays, which are another type of distributed delays whose lower and upper bounds are both limited, have been intensively investigated in [35], [38], [39].…”

Section: Problem Formulationmentioning

confidence: 99%

Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays

Liu

Wang

Liang

et al. 2013

IEEE Trans. Cybern.

168

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Abstract-In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete time-delays and the mode-dependent unbounded distributed time-delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete time-delays, distributed time-delays, mode transition probability and coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be solved efficiently by employing the semi-definite programme method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.

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A multistage reduction technique for feedback stabilizing distributed time-lag systems

Cited by 84 publications

References 9 publications

LMI based control design for linear systems with distributed time delays

LMI based control design for linear systems with distributed time delays

Delay Range Stability of distributed time delay systems

Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays

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