Seems like you want a general approach using math. I discuss some of it here. But M. J. S. Smith, "On the circuit analysis of the Schmitt trigger," in IEEE Journal of Solid-State Circuits, vol. 23, no. 1, pp. 292-294, Feb. 1988, doi: 10.1109/4.293 is a better bet for a correct approach. See Section II: General Analysis of Schmitt Trigger there.
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