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**On the uniform exponential stability of a wide class of linear time-delay systems.**
*(English)*
Zbl 1046.34086

The authors consider a general linear time-invariant system subject to point and distributed delay and to an impulsive function. Necessary and sufficient conditions for the global uniform stability (independent of delay) are given.

The proofs are based on conditions which guarantee that a linear operator on a Banach space is compact within a domain that contains the closed complex right-half plane provided that another one defined for the auxiliary system is also compact within a domain that contains the closed complex right-half plane. The paper contains a lot of explanatory remarks, special cases and examples.

The proofs are based on conditions which guarantee that a linear operator on a Banach space is compact within a domain that contains the closed complex right-half plane provided that another one defined for the auxiliary system is also compact within a domain that contains the closed complex right-half plane. The paper contains a lot of explanatory remarks, special cases and examples.

Reviewer: Josef DiblĂk (Brno)

### MSC:

34K20 | Stability theory of functional-differential equations |

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\textit{M. De la Sen} and \textit{N. Luo}, J. Math. Anal. Appl. 289, No. 2, 456--476 (2004; Zbl 1046.34086)

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### References:

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