Uniform stability of nonlinear systems with state-dependent delay

Li, Xiaodi; Peng, Dongxue

doi:10.1016/j.automatica.2021.110098

Cited by 11 publications

(1 citation statement)

References 19 publications

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“…It is a nonlinear system of differential equations with a time-dependent delay, where the control variable is the packet loss ratio. Although this work is much cited, it seems, to the best of our knowledge, that almost only linear approximations with constant delays have been exploited to propose various applicable AQM techniques (see, however, [Barbera et al(2010), Belamfedel Alaoui et al(2018), Li and Peng(2022)]). Let us restrict our short review to a few examples where this approximation has been employed:…”

Section: Introductionmentioning

confidence: 99%

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Mounier¹,

Join²,

Delaleau³

et al. 2023

Preprint

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Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the "round trip time", i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as a "flat output." All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward flatness-based control techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.

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Section: Introductionmentioning

confidence: 99%

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Mounier¹,

Join²,

Delaleau³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Stability analysis of stochastic differential systems with state‐dependent delay subject to average‐delay impulses

Xu,

Zhang,

2024

Math Methods in App Sciences

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In this paper, we study the stochastic weak local exponential stability of stochastic differential systems with state‐dependent delay (SDD) subject to average‐delay impulses by using Lyapunov–Krasovskii functional and stochastic analytical skill. Unlike time‐dependent delay discussed in the previous literature, we introduce SDD in impulsive stochastic differential systems, where SDD is a stochastic variable associated with system state, consequently leading to an indeterminate delay boundary. Our findings reveal that when destabilizing delayed impulses satisfying specific conditions are generated, the stability of stochastic differential systems with destabilizing delayed impulses and stable continuous stochastic dynamics can still be maintained. Additionally, if stable delayed impulses satisfy certain conditions, stability of the systems under consideration can also be achieved, irrespective of the stable status on the continuous stochastic dynamics. Finally, two examples are given to demonstrate the validity of theoretical results.

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Stability Analysis of Discrete‐Time Stochastic Systems With Markov Switching and State‐Dependent Delay

Fan,

Zhu

2024

Intl J Robust & Nonlinear

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This article focuses on the pth moment exponential stability of discrete‐time Markov switched stochastic systems with state‐dependent delay. By using Razumikhin technique, and stochastic analysis techniques, the state‐dependent delay with randomness due to the randomness of the system state can be addressed. With the help of stationary distribution of Markov switching and multiple Lyapunov–Krasovskii functionals approach, an appropriate switching rule is designed and a novel theorem on discrete‐time Markov switched stochastic systems with state‐dependent delay is established. Different from the previous results, the Markov switched with partially unstable subsystems and the state‐dependent delay with randomness are considered in this article, which brings many differences to the stability analysis of the system compared to traditional stability analysis. Furthermore, an illustrative example is performed to illustrate the effectiveness of the main theory.

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Uniform stability of nonlinear systems with state-dependent delay

Cited by 11 publications

References 19 publications

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Stability analysis of stochastic differential systems with state‐dependent delay subject to average‐delay impulses

Stability Analysis of Discrete‐Time Stochastic Systems With Markov Switching and State‐Dependent Delay

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