Affiliation:
1. Brno University of Technology, CEITEC - Central European Institute of Technology , Brno , Czech Republic
2. Taras Shevchenko National University of Kyiv , Kyiv , Ukraine
Abstract
Abstract
The paper studies absolute stability of neutral differential nonlinear systems
x
˙
(
t
)
=
A
x
t
+
B
x
t
−
τ
+
D
x
˙
t
−
τ
+
b
f
(
σ
(
t
)
)
,
σ
(
t
)
=
c
T
x
(
t
)
,
t
⩾
0
$$
\begin{align}\dot x(t)=Ax\left ( t \right )+Bx\left ( {t-\tau} \right ) +D\dot x\left ( {t-\tau} \right ) +bf({\sigma (t)}),\,\, \sigma (t)=c^Tx(t), \,\, t\geqslant 0
\end{align}
$$
where x is an unknown vector, A, B and D are constant matrices, b and c are column constant vectors, 𝜏 > 0 is a constant delay and f is a Lurie-type nonlinear function satisfying Lipschitz condition. Absolute stability is analyzed by a general Lyapunov-Krasovskii functional with the results compared with those previously known.
Reference60 articles.
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5. J. Baštinec, J. Diblík, D.Ya. Khusainov and A. Ryvolová, Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients, Bound. Value Probl. 2010 (2010) Article ID 956121, 20 pp., doi:10.1155/2010/956121.
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2 articles.
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