How can I model a time delay estimator and delay a signal by estimated delay when passed through this algorithm??

I'm trying to estimate the time delay as shown in the block below. Basically I have identified my reference mode as Discrete State Space and the Plant with Tau( as another Discrete State Space) and trying to create a time delay estimator in discrete time domain.

Continuous time domain when discretized becomes

Lets say I have xhat[k] and then when this is passed through time delay estimator, it should become xhat[k-tauhat]. For initially, this single step is where I'm stuck. I can't multiply xhat[k] and tauhat[k] - this would be incorrect.

Kindly advise me on this

[Kelvin Anto]

@Walter Roberson