Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Ayoub Cheddour; Abdelhai Elazzouzi; Fathalla A. Rihan

doi:10.1093/imamci/dnae027

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Ayoub Cheddour, Abdelhai Elazzouzi, Fathalla A. Rihan

Department of Mathematical Sciences

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

2 Citations (Scopus)

Abstract

The strong stabilization of the considered system is established by presenting sufficient conditions based on an observability condition expressed by the semigroup solution of the linear part of the bilinear system. An explicit estimate on the convergence of the decay rate is established. Moreover, some sufficient conditions are used to discuss the weak stabilization of the considered system. Additionally, an illustrative example with numerical simulations is included.

Original language	English
Pages (from-to)	611-633
Number of pages	23
Journal	IMA Journal of Mathematical Control and Information
Volume	41
Issue number	4
DOIs	https://doi.org/10.1093/imamci/dnae027
Publication status	Published - Dec 1 2024

Keywords

Banach state space
bilinear systems
decay estimate
distributed delay
feedback control
strong stabilization
weak stabilization

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Applied Mathematics

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10.1093/imamci/dnae027

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abstract = "The strong stabilization of the considered system is established by presenting sufficient conditions based on an observability condition expressed by the semigroup solution of the linear part of the bilinear system. An explicit estimate on the convergence of the decay rate is established. Moreover, some sufficient conditions are used to discuss the weak stabilization of the considered system. Additionally, an illustrative example with numerical simulations is included.",

keywords = "Banach state space, bilinear systems, decay estimate, distributed delay, feedback control, strong stabilization, weak stabilization",

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AU - Cheddour, Ayoub

AU - Elazzouzi, Abdelhai

AU - Rihan, Fathalla A.

PY - 2024/12/1

Y1 - 2024/12/1

N2 - The strong stabilization of the considered system is established by presenting sufficient conditions based on an observability condition expressed by the semigroup solution of the linear part of the bilinear system. An explicit estimate on the convergence of the decay rate is established. Moreover, some sufficient conditions are used to discuss the weak stabilization of the considered system. Additionally, an illustrative example with numerical simulations is included.

AB - The strong stabilization of the considered system is established by presenting sufficient conditions based on an observability condition expressed by the semigroup solution of the linear part of the bilinear system. An explicit estimate on the convergence of the decay rate is established. Moreover, some sufficient conditions are used to discuss the weak stabilization of the considered system. Additionally, an illustrative example with numerical simulations is included.

KW - Banach state space

KW - bilinear systems

KW - decay estimate

KW - distributed delay

KW - feedback control

KW - strong stabilization

KW - weak stabilization

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JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 4

ER -

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Abstract

Keywords

ASJC Scopus subject areas

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