an:01183174
Zbl 0913.34060
Hu, Guang-Da; Hu, Guang-Di
Stability of neutral delay-differential systems: Boundary criteria
EN
Appl. Math. Comput. 87, No. 2-3, 247-259 (1997).
00049262
1997
j
34K20 34K40 34K10
linear neutral delay differential equations; asymptotic stability criteria; boundary criteria
For linear neutral delay differential equations of the form
\[
\dot{x}(t)=Ax(t)+Bx(t-\tau)+C\dot{x}(t-\tau),
\]
where \(x:{\mathbb{R}}_+\to{\mathbb{R}}^n\) is an unknown function, \(A\), \(B\) and \(C\) are constant \(n\times n\)-matrices and \(\tau=\text{ const}>0\), a series of delay dependent asymptotical stability criteria are given. The criteria are based on the evaluation of a real-valued function on the boundary of a rectangle in the complex plane.
R.R.Akhmerov (Novosibirsk)