  Absolute exponential stability problem of delay time-varying systems (DTVS)
with sector-bounded nonlinearity is presented in this paper. By using the
comparison principle and properties of positive systems we derive several novel
criteria of absolute exponential stability, for both continuous-time and
discrete-time nonlinear DTVS. When applied to the time-invariant case, the
obtained stability criteria are shown to cover and extend some previously known
results, including, in particular, the result due to S.K. Persidskii in
Ukrainian Mathematical Journal, vol. 57(2005). The theoretical results are
illustrated by examples that can not be treated by the existing ones.
