Abstract
Let [Formula: see text] and [Formula: see text] be bounded operators in a Banach space. For the equation [Formula: see text] we derive sharp explicit delay-dependent exponential stability conditions via the commutator [Formula: see text]. 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.
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