Stabilization of distributed systems via bilinear boundary control

Benoudi, Mustapha; Zerrik, El Hassan; Larhrissi, Rachid

doi:10.1002/mma.8981

Math Methods in App Sciences

2023

DOI: 10.1002/mma.8981

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Stabilization of distributed systems via bilinear boundary control

Mustapha Benoudi

El Hassan Zerrik

Rachid Larhrissi

Abstract: In this paper, the focal point is to study the stabilization problem of distributed systems via bilinear boundary control. Hence, we give some sufficient conditions to ensure weak, strong, and exponential stabilization of the considered system. Finally, an example of application is devoted, and the attained results are illustrated through numerical simulations.

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Cited by 7 publications

References 21 publications

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Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

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Math Methods in App Sciences

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Applying delayed dynamical models to characterize the dynamics of neural networks has attracted great interest from scientific community. In this current manuscript, a kind of new tri‐neuron bidirectional associative memory (BAM) neural networks including delay are formulated. The properties of solution and Hopf bifurcation issue of the established tri‐neuron BAM neural networks including delay are investigated. First, we check the existence and uniqueness of the solution to the formulated delayed tri‐neuron BAM neural networks by virtue of fixed point theorem. Second, we seek the boundedness of the solution of the formulated delayed tri‐neuron BAM neural networks in view of a suitable function and inequality skills. Third, the delay‐independent criteria on stability and bifurcation of the formulated delayed tri‐neuron BAM neural networks are acquired. Fourth, Hopf bifurcation control aspect of the formulated delayed tri‐neuron BAM neural networks is explored via designing two proper hybrid controllers. To prove the accuracy of gained primary assertions, software simulation experiments are put into practice.

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Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

Cui

et al. 2023

Math Methods in App Sciences

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Novel extended mixed controller design for bifurcation control of fractional‐order Myc/E2F/miR‐17‐92 network model concerning delay

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et al. 2023

Math Methods in App Sciences

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MiR‐17‐92 has a vital effect on the adjustment of the Myc/E2F protein in chemistry. In this work, we propose a novel fractional‐order delayed Myc/E2F/miR‐17‐92 network model that revels the relation between miR‐17‐92, E2F, and Myc. Taking advantage of Laplace transform, we obtain the characteristic equation of the established fractional‐order delayed Myc/E2F/miR‐17‐92 network model. By virtue of stability theorem and bifurcation criterion of fractional‐order dynamical equation, a novel delay‐independent condition guaranteeing the stability and the generation of bifurcation phenomenon of the involved model is acquired. By exploiting a proper extended mixed controller (including controller and delayed feedback controller), we efficiently control the stability domain and the emergence of bifurcation for the the involved model. By utilizing another suitable extended mixed controller (including controller and hybrid controller), we can successfully adjust the stability domain and the emergence of bifurcation for the the involved model. The research indicates that delay plays a vital role in stabilizing system and controlling bifurcation of the fractional‐order delayed Myc/E2F/miR‐17‐92 network model. Computer experiment results illustrate the scientificity of the gained key analytical outcomes. The acquired results in this research are totally innovative and own immense theoretical meaning in regulating the concentrations of different proteins.

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Fractional output stabilization of distributed bilinear systems with a time delay

Benoudi,

Larhrissi

2023

Rend. Circ. Mat. Palermo, II. Ser

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Stabilization of distributed systems via bilinear boundary control

Cited by 7 publications

References 21 publications

Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

Novel extended mixed controller design for bifurcation control of fractional‐order Myc/E2F/miR‐17‐92 network model concerning delay

Fractional output stabilization of distributed bilinear systems with a time delay

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