Stochastic adaptive control and prediction based on a modified least squares--The general delay-colored noise case

In [1], global convergence for a stochastic adaptive control based on modified least-squares algorithms has been established. However, the proof of Lemma 3.4 in [1] is questionable. A similar question existed in the proof of
\delta(t - d) \rightarrow 0
in [2]. Without using this conclusion, the present note attempts to establish global convergence for a discrete-time stochastic adaptive control and prediction based on slightly modified least-squares algorithms for linear time-invariant discrete-time systems having general delay and colored noise.