Delay-dependent stability conditions for differential-difference equations with small commutators in a banach space

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Abstract

Let <FOR VERIFICATION>A and <FOR VERIFICATION>B be bounded operators in a Banach space. For the equation <FOR VERIFICATION>du(t)/dt = Au(t) + Bu(t - h)(h > 0) we derive sharp explicit delay-dependent exponential stability conditions via the commutator <FOR VERIFICATION>AB - BA. The stability conditions in terms of the commutator enable us to construct a feedback with delay, which stabilizes a system. Gives us a possibility construct Stabilization of Systems with Retarded Feedback in a Banach Space. Our results are new even in the finite-dimensional case.

Original languageEnglish
Article number2350009
JournalBulletin of Mathematical Sciences
DOIs
StateAccepted/In press - 1 Jan 2023

Keywords

  • Banach space
  • commutator
  • differential-delay equation
  • stability

ASJC Scopus subject areas

  • General Mathematics

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