Using (13), we obtain that where Integrating inequality (14) from t − 1 to t , we get Since z ( t ) is nonincreasing for t > T, from the above inequality, we obtain that and so, we have Using (15), (8), and (9), we obtain from the above inequality that and 8 t ∫ t − 1 ∏ [ s − 1] <t$_{j}$ ≤ s (1 − b$_{j}$ ) c ( s $_{) exp}$   s ∫ [ s − 1] a ( u ) $_{du}$   ds ≤ 1 . t ∫ t − 1 ∏ s − τ<t$_{j}$ ≤ s (1 − b$_{j}$ ) b ( s $_{) exp}$  s ∫ s − τ a ( u ) $_{du}$  ds ≤ 1 , (16) t ∫ t − 1 P ( s ) ds ≤ 1 . z ( t ) + z ( t − $_{1)}$  t ∫ t − 1 P ( s ) ds − $_{1}$  ≤ 0 z ( t ) − z ( t − 1) + t ∫ t − 1 P ( s ) z ( s − 1) ds ≤ 0 . P ( t ) = B ( t $_{) exp}$  t ∫ t − τ a ( s ) $_{ds}$  + C ( t $_{) exp}$   t ∫ [ t − 1] a ( s ) $_{ds}$   . (15) 0 = z $^{′}$( t ) + B ( t ) z ( t − τ $_{) exp}$  t ∫ t − τ a ( s ) $_{ds}$  + C ( t ) z ([ t − $_{1]) exp}$   t ∫ [ t − 1] a ( s ) $_{ds}$   ≥ z $^{′}$( t ) + z ( t − 1) P ( t ) , (14)