Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov–Razumikhin Method

Nekhoroshikh, Artem; Efimov, Denis; Polyakov, Andrey; Perruquetti, Wilfrid; Furtat, Igor B.

doi:10.1109/tac.2022.3168487

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A Ilf-based Finite-time Control With Inverse Optimality1

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2024

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Cited by 9 publications

(1 citation statement)

References 17 publications

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“…Theorem 2: Consider the high-order system (3) with the ILF-based controller (23) and the ILF in (21). Denote…”

Section: A Ilf-based Finite-time Control With Inverse Optimalitymentioning

confidence: 99%

Event-triggered Finite-time Control Using Inverse-optimal Implicit Lyapunov Function

Wang¹,

Ge²,

Zhang³

2022

Preprint

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This work deals with the event-triggered finite-time control for high-order systems based on an implicit Lyapunov function (ILF). With the construction of an inverse optimal problem, a novel expression of ILF is obtained. By designing the event-triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally finitetime stable and there exists no Zeno phenomenon. Extensions to the scenario with a multi-agent system are studied where a finite-time tracking control drives all the agents to reach a consensus. The obtained theoretical results are supported by numerical simulations.

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“…Theorem 2: Consider the high-order system (3) with the ILF-based controller (23) and the ILF in (21). Denote…”

Section: A Ilf-based Finite-time Control With Inverse Optimalitymentioning

confidence: 99%

Event-triggered Finite-time Control Using Inverse-optimal Implicit Lyapunov Function

Wang¹,

Ge²,

Zhang³

2022

Preprint

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Stability analysis and integral extension of sub‐optimal nonlinear damping control

Efimov,

Ruderman

2024

Intl J Robust & Nonlinear

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The problems of robustness with respect to external inputs and of convergence rate estimation are considered for the so‐called sub‐optimal nonlinear damping control. To this end, existence of solutions is justified, a strict Lyapunov function is found and its properties are investigated. The hyperexponential convergence of the unperturbed sub‐optimal nonlinear damping control is demonstrated. Moreover, an integral extension is proposed to complement the controller with capability of compensation for static errors. The results are illustrated by numeric simulations and the control experiments.

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Fixed-Time Stability of Time-Varying Hybrid Systems with Time-Delay

Chen,

Yang

2024

Circuits Syst Signal Process

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Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov–Razumikhin Method

Cited by 9 publications

References 17 publications

Event-triggered Finite-time Control Using Inverse-optimal Implicit Lyapunov Function

Event-triggered Finite-time Control Using Inverse-optimal Implicit Lyapunov Function

Stability analysis and integral extension of sub‐optimal nonlinear damping control

Fixed-Time Stability of Time-Varying Hybrid Systems with Time-Delay

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