Feedback response in linear system
What do you recommend ? – user185674


I can only tell you that I use a circuit simulator called micro-cap 12 (free now) and that it can be used with laplace terms i.e. you can create blocks with all manner of s terms inside. Then I would abruptly change "a" and see how the output response changed. 

For instance, here's a simple example of a 2nd order low pass filter with 1:1 negative feedback fed from a 1 volt biased square wave of 1 Hz: -



And the transient response looks like this: -



You can add "K" within the feedback loop and then make K suddenly rise to K+a and see how the response changes. See example below: -



I've added a multiplier in the feedback loop fed from a battery that sets the multiplication value to K+a. But, there's no reason whay the battery cannot be replaced by a voltage source that stepped from a value of K to K+a.

And, just in case anyone doubts micro-cap's ability to perform this sort of task, here's a pretty picture from the sales blurb: -