On a sufficient condition for finite-time partial stability and stabilization: applications

Jammazi, Chaker

doi:10.1093/imamci/dnp025

Cited by 33 publications

(21 citation statements)

References 33 publications

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“…Different results of finite-time controller designing have been already obtained with different techniques and methodologies [15,23,24,26,27,31,32]. Since the proposed theorem gives a new form for the Lyapunov function, the effectiveness of the algorithm developed in this paper is demonstrated with a design example and a computer simulation for the three common cases: the single, double and triple integrators.…”

Section: Simulations Of the Controllermentioning

confidence: 97%

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Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

Khelil¹,

Otis²

2016

Preprint

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This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback, which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system finite-time stable. The proof is based on a recursive design algorithm developed recently to construct the virtual Hölder continuous, finite-time stabilizer as well as a C 1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems.

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Section: Simulations Of the Controllermentioning

confidence: 97%

“…We also recall the Lyapunov theorem of finite-time stability, which gives a necessary and sufficient condition for non-Lipschitz continuous autonomous systems to be finite-time stable [15,18,19,26,27]. …”

Section: Finite-time Stabilitymentioning

confidence: 99%

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

Khelil¹,

Otis²

2016

Preprint

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“…It was proved in [40] that this theory is a natural extension of the classical concept of stability in Lyapunov sense. Stability with respect to the part called also "partial stability" has been intensively studied since Lyapunov in 1898, see for example [28,29,55,65,68].…”

Section: Introductionmentioning

confidence: 97%

“…(1) Time-varying periodic controllers [9,20,22,24,25,[46][47][48]53,57,58,61]; (2) Discontinuous feedback laws [5,6,17,27,64]; (3) Partial asymptotic or finite-time stabilization by differentiable or continuous static feedback laws [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

“…It consists of the concept of the partial asymptotic stabilization (PAS), this concept means the asymptotic stabilization with respect to the maximum components of the system while the remaining components are convergent to some positions depending on the initial conditions. The PAS concept is interesting from a practical point of view, see for instance [36,37,40].…”

Section: Introductionmentioning

confidence: 99%

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A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator

Jammazi

2011

ESAIM: COCV

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Abstract.We consider chained systems that model various systems of mechanical or biological origin.It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or discontinuous feedbacks) to ensure the asymptotic stability even in finite time for some variables, while other variables do converge, and not necessarily toward equilibrium. Furthermore, we build feedbacks that permit to vanish the two first components of the Brockett integrator in finite time, while ensuring the convergence of the last one. The considering feedbacks are continuous and discontinuous and regular outside zero.Mathematics Subject Classification. 93D15, 93C10, 93D09.

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Finite-Time Stabilization of Some Classes of Infinite Dimensional Systems

Najib,

Ouzahra

2023

Trends in Mathematics

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On a sufficient condition for finite-time partial stability and stabilization: applications

Cited by 33 publications

References 33 publications

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator

Finite-Time Stabilization of Some Classes of Infinite Dimensional Systems

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