Lyapunov–Krasovskii functionals for homogeneous time delay systems of neutral type

Аlexandrova, Irina V.; Zhabko, Alexey P.

doi:10.1002/rnc.5684

Cited by 3 publications

(6 citation statements)

References 31 publications

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“…The delay is undoubtedly essential to affect the system's performance among these factors. Therefore, constant delay and time‐varying delay have challenging problems to be solved 6‐9 . In Reference 6, the issue of network synchronization of nonlinear systems interconnected through diffusive time‐delayed dynamic couplings has been addressed.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, constant delay and time-varying delay have challenging problems to be solved. [6][7][8][9] In Reference 6, the issue of network synchronization of nonlinear systems interconnected through diffusive time-delayed dynamic couplings has been addressed. And Reference 7 has applied impulsive synchronization into chaos-based secure communication with the presence of both the transmission delay and sampling delay.…”

Section: Introductionmentioning

confidence: 99%

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Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

Jiang

Alofi

et al. 2023

Intl J Robust & Nonlinear

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Summary Over the past decades, various successful results have shown the discoveries and progress of impulsive synchronization. Yet, little attention has been devoted to the effects of the impulsive elasticity coefficient on network synchronization for both impulsive control problems and impulsive disturbance problems. In this work, we study impulsive pinning synchronization for coupled neural networks from a large delay perspective. Some flexible synchronization criteria are derived based on the average impulsive interval method. It has shown that synchronization of coupled neural networks with arbitrarily finite delay can be achieved via controlling a small fraction of nodes. Specifically, by applying a strict comparison principle for impulsive delayed neural networks, the effects of the impulsive elasticity coefficient on synchronization are revealed to be dissimilar from the case of delay‐free neural networks. One can verify that increasing the elasticity coefficient may bring a desynchronizing impact on the original synchronized networks. More ulteriorly, the generated criteria will still hold if the delay is sufficiently large, which implies that the delay is independent of the size of the impulsive interval. Our work is an essential step toward investigating the role of the elasticity coefficient on synchronization. Furthermore, the synchronization region of different impulsive weights, impulsive intervals, and impulsive control proportions are described thoroughly.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

Jiang

Alofi

et al. 2023

Intl J Robust & Nonlinear

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“…Lyapunov‐Krasovskii functional based approaches have been commonly used to deal with time delays in continuous time. These approaches have been extensively studied in both theory and applications 8 . Considering sensor to controller delay problem, Zhao et al 9 proposed a mean square asymptotic stability controller for networked control systems, in which Lyapunov‐Krasovskii functional was adopted in the stability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…These approaches have been extensively studied in both theory and applications. 8 Considering sensor to controller delay problem, Zhao et al 9 proposed a mean square asymptotic stability controller for networked control systems, in which Lyapunov-Krasovskii functional was adopted in the stability analysis. Mohammadi et al 10 adopted a high-dimensional integral Lyapunov-Krasovskii functional to design an adaptive controller for MIMO systems with time delays and dead-band inputs.…”

Section: Introductionmentioning

confidence: 99%

Robust lateral motion control of distributed drive vehicle considering long input delays

Xie

et al. 2022

Intl J Robust & Nonlinear

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This article presents a comparative study of lateral motion controller design for distributed drive vehicle. Aiming at handling long input delays, two types of robust controllers are specifically investigated. First, a Lyapunov-Krasovskii functional based robust controller design is proposed. Considering input delay, the design conditions of the state-feedback controller are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved using LMI toolbox. Second, based on the same control law, a robust predictive controller design is further presented. However, different from the Lyapunov-Krasovskii functional based robust controller, the control gain of the proposed robust predictive controller is calculated without considering the input delay. An input delay estimator and a predictor are developed instead to reconstruct the delay-dependent state, which is further used to generate a new feedback error. Moreover, the feasibility of this control scheme is theoretically proved. Finally, extensive co-simulations with Carsim and Matlab/Simulink are conducted to compare the performance between these two controllers. Compared with the Lyapunov-Krasovskii functional based robust controller, longer input delay can be handled by using the proposed robust predictive controller.

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“…Известно, что и при отсутствии переключений прямой метод Ляпунова, расширенный Н. Н. Красовским на случай наличия запаздываний, требует нестандартного подбора функционалов под конкретные типы систем. Например [12], для особого класса однородных систем предложен подход к построению функционалов, дающих оценку области притяжения и решениям. Достаточные условия асимптотической устойчивости широкого класса нелинейных систем с сосредоточенным запаздыванием получены [13] за счет объединения подходов Ляпунова -Красовского и Разумихина.…”

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Stability of Lurie-type systems with asynchronous and synchronous switching and constant delays

Andriyanova

2023

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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The problems of analysis for systems with synchronous and asynchronous switching have been actively studied for the linear case. In this paper, a switched system of difference-differential equations, in which the right-hand side consists of a linear term and an essentially nonlinear part containing sector-type components is considered. This kind of systems belongs to the class of Lurie indirect control systems. Sufficient conditions on the system parameters and the switching law are investigated for asymptotic stability to be guaranteed both in the case of synchronous switching between subsystems and in asynchronous one. In the latter case it is supposed that the nonlinear delayed part switches with a lag equal to the corresponding delay. It is required that stability should be preserved for any constant positive delays. The problem is solved using the Lyapunov — Krasovsky approach. The functional is chosen that includes a quadratic form and integrals of nonlinearities. Restrictions that ensure asymptotic stability for an arbitrary switching law are found. With such an approach for the asynchronous case these conditions turn out to be less restrictive. By using multiple functionals the restrictions on the lengths of intervals between switchings are also obtained. This type of conditions are similar for both cases of synchronous and asynchronous switching. Theoretical results are demonstrated by a specially selected example.

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Lyapunov–Krasovskii functionals for homogeneous time delay systems of neutral type

Cited by 3 publications

References 31 publications

Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

Robust lateral motion control of distributed drive vehicle considering long input delays

Stability of Lurie-type systems with asynchronous and synchronous switching and constant delays

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