On the LTI properties of adaptive feedforward systems with tapdelay-line regressors

It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N^-1, where N is the number of taps. Hence, the adaptive system becomes LTI in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new “LTI plus norm-bounded perturbation” representation renders, for the first time, the adaptive system analyzable by standard robust control methods