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Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems. (English) Zbl 1124.34049
The authors investigate the asymptotic stability of the following neutral system: $\begin{cases}\dot x(t)-C\dot x(t-\tau)=Ax(t)+A_dx(t-\tau),\quad t>0,\\ x(t)=\phi(t),\quad t\in[-\tau,0],\end{cases}$ where $$x(.)\in{\mathbb R}^n$$ is the state vector; $$\tau>0$$ is the constant time delay, and $$A,A_d,C$$ are constant matrices with appropriate dimensions. $$\phi(.)$$ denotes an initial condition which is a continuous vector-valued function of $$t\in[-\tau,0]$$.
An augmented Lyapunov functional, which takes into account the delay term is proposed. It gives delay-independent criteria for asymptotic stability.
Numerical examples are also given.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations
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