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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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