What is the maximal acceptable delay between pilot's input and flight control surface actuation? While I was watching a cockpit video of an A330 landing in which the pilot was frenetically moving its sidestick,  I wander what was the reaction time of this flight by wire system. Indeed, the time for transmiting the signal from the sidestick to flight computer, the time for computer  to  interpret all its inputs (pilot's  input, probes,...) and to decide to act on flight control surfaces, the aircraft's reaction is not instantaneous.

Then, I realize that whatever the transmission system, there are delay between pilot's input and air control surfaces movement (material's elasticity, time for hydraulic fluid to transmit pressure, other mechanism I can't imagine).

Thus my question is: is there a maximal delay between pilot's input and flight control surface deflection to certify an aircraft? 

If needed, for the FBW system, a direct law can be considered (no complex computation as flight control surface movement is proportional to input)

If needed, the question can be restricted to airliners flying under FAA and EASA jurisdictions.

EDIT: given the first feedback (comments, edits, answer), I want to highlight this question is not restricted to fly-by-wire (transmitting pilot's input through mechanical links may also induce delay)

EDIT: I think I didn't emphasize enough that this question is only about delay between pilot's input and control surface reaction. I understand that this delay is negligible compared to all other delay, but this is the one the question focus on.
Excessive phase lag is a direct contributor to Type I Pilot-Induced Oscillation (PIO). Phase lag comes from:


Rigid body dynamics of the aircraft (e.g. delay between elevator surface and pitch rate response)
Actuators (finite acceleration time between input and desired surface angle)
Structural compliance (e.g. cable friction)
Transport delay in signals
Finite computational bandwidth (e.g. loop closure bandwidth)


From NASA Report 4683, PIO susceptibility can be expressed assuming the pilot is compensatory; that is, the pilot input and the aircraft response would be exactly in phase, except for a constant time delay (across frequencies). This model is expressed as:

$$G(s)=\frac{K}{s}e^{-\tau_e s}$$

where $\tau_e$ is the effective time delay, or equivalently, phase rate as a function of frequency

From its research, it found that an effective time delay larger than 0.3 sec leads to PIO issues. Given a typical pilot time delay of 0.2 sec, this would imply an upper bound aircraft effective time delay of 0.1 sec at higher frequency (around 5 rad/s), end to end.