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Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients. (English) Zbl 1214.34059

The paper deals with the linear systems of neutral differential equations with constant coefficients and a constant delay of the form

$\stackrel{˙}{x}\left(t\right)=D\stackrel{˙}{x}\left(t-\tau \right)+Ax\left(t\right)+Bx\left(t-\tau \right),$

where $t\ge 0$, $\tau >0$, $A,B,$ and $D$ are $n×n$ constant matrices, and $x:\left[-\tau ,\infty \right)\to {ℝ}^{n}$ is a column vector-solution. The authors investigate the exponential-type stability of such systems using Lyapunov-Krasovskii type functionals. Delay-dependent conditions sufficient for the stability are formulated in terms of positivity of auxiliary matrices. Illustrative examples are shown and comparisons with known results are given.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations 34K06 Linear functional-differential equations
##### References:
 [1] [2]