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px941934

With time-varying discrete delay of single species model with feedback control global stability

V l +,. . (t) ≤ a c (t) Iu (t) a (t) l + T_I (t) A y (t) I now define V (t) = V. (t) +. (t), the results from previous shows : DV (t) ≤ a A (t) l (t) A y (t) l-B (t) lI /, (t) A t, (t) l (t ≥ + r) where : A (t) and B (t) as the conditions of Theorem 1 in the definition. Suppose there exists by the theorem of a> 0 and ≥ T + r, such that when ≥ + r , there is A (t) ≥ port > 0, B (t) ≥ port > 0 , which was integral to the above inequality : (T) a (') ≤ a I. 【 A (s) l (s) A y (s) l + at (s) lu (s) a t,[link widoczny dla zalogowanych], (s) l 】 ds (t ≥ T ') is (t) + port I. 【 I (s) A y (s) I + lu (s) a (s) I 】 ds ≤ V (T ') (t ≥ T') that V (t) in [', + ∞) is bounded on And I. 【 l (s) A y (s) I + Iu (s) a (s) I 】 ds <+ ∞, thus , the use of n 】 Barbalat lemma , we can get : lira 【 I (t) A y (t ) l + lI /, (t) a (t) l 】 = 0 is proved.