# Stability results for abstract evolution equations with intermittent time-delay feedback

## TL;DR

This paper investigates the stability of abstract evolution equations with intermittent time-delay feedback, demonstrating conditions under which the system remains stable or becomes exponentially stable, supported by concrete examples.

## Contribution

It provides new stability criteria for evolution equations with on-off delay feedback, extending existing results to cases with intermittent delays.

## Key findings

- System remains asymptotically stable under certain delay conditions.
- Exponential stability achieved with additional assumptions.
- Concrete examples illustrate the theoretical results.

## Abstract

We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the system remains asymptotically stable. Under additional assumptions exponential stability results are also obtained. Concrete examples illustrating the abstract results are finally given.