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How should we conduct a perturbation test for an LTI unknown system by perturbing the input to see the output response i.e. How many different perturbation step size should be given to the input?

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    $\begingroup$ In general, it's a good idea to include the physical system description. I had a friend who had to put in a control system for a large radar antenna; which was perfectly capable of tearing itself apart if commanded incorrectly. Touchy! He wrapped a very slow control loop around the antenna to position and stabilize it, and then he injected a very low level of noise and did a cross-correlation of input versus output. Worked out fine. HP/Agilent made an instrument that was designed for this type of analysis. The point is, the methods vary with the application/reality. $\endgroup$ – rrogers Aug 9 '16 at 21:12

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