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Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations. (English) Zbl 1187.37124

The stability criteria for the following neutral systems with mixed time-varying delays and nonlinear perturbations are discussed

$\stackrel{˙}{x}\left(t\right)=Ax\left(t\right)+Bx\left(t-h\left(t\right)\right)+C\stackrel{˙}{x}\left(t-\tau \left(t\right)\right)+{f}_{1}\left(x\left(t\right),t\right)+{f}_{2}\left(x\left(t-h\left(t\right)\right),t\right)+{f}_{3}\left(\stackrel{˙}{x}\left(t-\tau \left(t\right)\right),t\right),$
$x\left(\theta \right)=\varphi \left(\theta \right),\phantom{\rule{2.em}{0ex}}\stackrel{˙}{x}\left(\theta \right)=\varphi \left(\theta \right),\phantom{\rule{2.em}{0ex}}\forall \theta \in \left[-max\left(h,\tau \right),0\right]·$

The authors are particularly interested in nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on Lyapunov functional approach and linear matrix inequalities, the authors derive the less conservative delay-dependent stability conditions. The corresponding asymptotic stability theorems are formulated. The proposed criteria are both neutral-delay dependent and discrete dependent, and at the same time, are dependent on the derivative of the discrete and neutral delays. The numerical examples demonstrating the effectiveness of the proposed method are also discussed.

##### MSC:
 37N25 Dynamical systems in biology 92B20 General theory of neural networks (mathematical biology)
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