Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type

Leonid Berezansky; Josef Diblík; Zdeněk Svoboda; Zdeněk Šmarda

doi:10.1016/j.jfranklin.2022.11.012

Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type

Leonid Berezansky, Josef Diblík, Zdeněk Svoboda, Zdeněk Šmarda

Department of Mathematics

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

2 Scopus citations

Abstract

Linear neutral vector equations x˙(t)=A₀(t)x˙(h₀(t))+∑k=1mA_k(t)x(h_k(t))+∫_g(t)^tP(t,s)x(s)dsare considered on interval [0,∞). Here x=(x₁,…,x_n)^T, m is a positive integer, the entries of matrices A_l, l=0,…,m, P, and the delays h_k, k=0,…,m, g are assumed to be Lebesgue measurable functions. New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.

Original language	English
Pages (from-to)	301-326
Number of pages	26
Journal	Journal of the Franklin Institute
Volume	360
Issue number	1
DOIs	https://doi.org/10.1016/j.jfranklin.2022.11.012
State	Published - 1 Jan 2023

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2022.11.012

Cite this

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title = "Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type",

abstract = "Linear neutral vector equations x˙(t)=A0(t)x˙(h0(t))+∑k=1mAk(t)x(hk(t))+∫g(t)tP(t,s)x(s)dsare considered on interval [0,∞). Here x=(x1,…,xn)T, m is a positive integer, the entries of matrices Al, l=0,…,m, P, and the delays hk, k=0,…,m, g are assumed to be Lebesgue measurable functions. New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.",

author = "Leonid Berezansky and Josef Dibl{\'i}k and Zden{\v e}k Svoboda and Zden{\v e}k {\v S}marda",

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T1 - Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Svoboda, Zdeněk

AU - Šmarda, Zdeněk

PY - 2023/1/1

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N2 - Linear neutral vector equations x˙(t)=A0(t)x˙(h0(t))+∑k=1mAk(t)x(hk(t))+∫g(t)tP(t,s)x(s)dsare considered on interval [0,∞). Here x=(x1,…,xn)T, m is a positive integer, the entries of matrices Al, l=0,…,m, P, and the delays hk, k=0,…,m, g are assumed to be Lebesgue measurable functions. New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.

AB - Linear neutral vector equations x˙(t)=A0(t)x˙(h0(t))+∑k=1mAk(t)x(hk(t))+∫g(t)tP(t,s)x(s)dsare considered on interval [0,∞). Here x=(x1,…,xn)T, m is a positive integer, the entries of matrices Al, l=0,…,m, P, and the delays hk, k=0,…,m, g are assumed to be Lebesgue measurable functions. New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.

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Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type

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