Comments on "Robust stabilization of a class time-delay nonlinear systems"

From the coordinates transformation, we can see that only after i 1 (ri 1 (t)) is obtained can hi (ri (t )) be obtained. After we obtain hi (ri (t )) ; ~ ij (rj (t )) can be determined from (6). In other words, ~ ij (rj (t )) can not be determined until i 1 (ri 1 (t)) is obtained. However, from the iterative procedure in the main result of [1], we can see that function i 1 (ri 1 (t)) is obtained by an iterative method similar to backstepping method. That is, we can obtain 1 (z1 (t)) is step 1 (15 in paper [1]), 2 (r2 (t)) in step 2 ([1, 27]), . . ., k (rk (t)) in step k; . . .. So, from the procedure we can know that in step i, we can not obtain k (rk (t)) when k > i, that is, in step i, we cannot obtain hk (rk (t )), so ~ ki (ri (t )) also can not be obtained. However, in the proof of [1, Th. 3.1], the author used unknown ~ ki (ri (t )) to construct Lyapunov–Krasovskii function and obtained corresponding i (ri (t)) in step i (k > i). For example, in step 1, the Lyapunov–Krasovskii function was