Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

Bacem Ben Nasser; Mohamed Djemai; Michael Defoort; Taous-Meriem Laleg-Kirati

doi:10.1080/00207721.2020.1869345

Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

Bacem Ben Nasser, Mohamed Djemai, Michael Defoort, Taous-Meriem Laleg-Kirati

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales.

Original language	English (US)
Pages (from-to)	1-11
Number of pages	11
Journal	International Journal of Systems Science
DOIs	https://doi.org/10.1080/00207721.2020.1869345
State	Published - Feb 8 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-02-16
Acknowledged KAUST grant number(s): BAS/1/1627-01-01
Acknowledgements: Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) through the base research fund under [grant number BAS/1/1627-01-01].

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10.1080/00207721.2020.1869345

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title = "Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances",

abstract = "This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales.",

author = "{Ben Nasser}, Bacem and Mohamed Djemai and Michael Defoort and Taous-Meriem Laleg-Kirati",

note = "KAUST Repository Item: Exported on 2021-02-16 Acknowledged KAUST grant number(s): BAS/1/1627-01-01 Acknowledgements: Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) through the base research fund under [grant number BAS/1/1627-01-01].",

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doi = "10.1080/00207721.2020.1869345",

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AU - Ben Nasser, Bacem

AU - Djemai, Mohamed

AU - Defoort, Michael

AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2021-02-16 Acknowledged KAUST grant number(s): BAS/1/1627-01-01 Acknowledgements: Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) through the base research fund under [grant number BAS/1/1627-01-01].

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Y1 - 2021/2/8

N2 - This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales.

AB - This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales.

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SP - 1

EP - 11

JO - International Journal of Systems Science

JF - International Journal of Systems Science

ER -

Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

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