In the bode plot of control systems , how can i calculate the maximum forward path time delay?
A bode plot is in fact two plots, one of magnitude and one of phase angle. Here's one of a 2nd order low pass filter: -



At 0dB on the magnitude plot, the corresponding phase angle is about -150 degrees i.e. a phase margin of 30 degrees; that is to say it's 30 degrees away from becoming an oscillator (that's a "don't want").

Now imagine this were your open loop response and you applied non-phase changing feedback - it would not oscillate and that's a good thing. However if you put a delay in the forward path it would step it closer to the oscillation point. 

For example, in the picture above the unity gain is at about 5 radians per second (call it 1 Hz) and, at 1 Hz if you added a forward time delay of about one-twelvth of a second you would delay a 1 Hz signal by 30 degrees of its cycle. Phase margin would now be zero and you have a margnial oscillator.

So, you have to take your formulas for forward gain and draw a bode plot then find the phase margin, then equate that phase margin to a time delay at the particular frequency the gain falls to unity and, that time delay is the borderline maximum time delay your system can suffer when the feedback is in place.

You don't have to draw a bode plot of course; you can do it in the algebra.