Abstract
It is shown that every asymptotically equistable linear time-varying infinite-dimensional discrete-time system x k+1 = A k x k is uniformly asymptotically equistable, if A k is a collectively compact sequence of bounded linear operators. Next, this result is used to prove that for a broad class of linear retarded functional differential equations, the notions of asymptotic equistability and uniform asymptotic equistability coincide.
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