# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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)