Differential and Integral Equations

Stability of the solution semigroup for neutral delay differential equations

Richard Fabiano and Catherine Payne

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We derive a new condition for delay-independent stability of systems of linear neutral delay differential equations. The method applies ideas from linear semigroup theory, and involves renorming the underlying Hilbert space to obtain a dissipative inequality on the infinitesimal generator of the solution semigroup. The new stability condition is shown to either improve upon or be independent of existing stability conditions.

Article information

Differential Integral Equations, Volume 31, Number 1/2 (2018), 133-156.

First available in Project Euclid: 26 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K06: Linear functional-differential equations 34K40: Neutral equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Fabiano, Richard; Payne, Catherine. Stability of the solution semigroup for neutral delay differential equations. Differential Integral Equations 31 (2018), no. 1/2, 133--156. https://projecteuclid.org/euclid.die/1509041405

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