Application of ramp frequency
I don´t think that applying such a frequency ramp to any device can reveal its stability properties. If a circuit is unstable, it will oscillate or remain in a kind of saturation - independent on the excitation at its input..

However, a very important application of such a frequency sweep is to measure the frequency response of filters - for example, in conjunction with signal analyzers.
Thus, you are able t display the transfer curve (amplitude and/or phase vs. frequency) on the screen.