# 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)
Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays. (English) Zbl 1241.34080

The problem of exponential stability and stabilization is studied for a class of uncertain linear systems with time-varying delay. The time delay is a continuous function belonging to a given interval, which means that the lower and the upper bounds for the time-varying delay are available.

The distinctive features of the presented results are, by the author’s opinion, the following: the delay function is not necessary to be differentiable and the lower bound of the delay is not restricted to be zero. Notice that, in the most delay-dependent stability results for systems with time-varying delay, the time delay function is required to be differentiable and, moreover, the upper bound of the derivative is restricted to a number less than unity.

Based on the construction of some Lyapunov-Krasovskii functionals, new delay-dependent sufficient conditions for the exponential stabilization of the systems are established in terms of LMIs. Numerical examples are given to demonstrate the effectiveness of the derived conditions.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K06 Linear functional-differential equations 34K27 Perturbations of functional-differential equations 34K35 Functional-differential equations connected with control problems