The stability radius of a continuous function f (in a functional space F) with respect to an open stability domain D is the distance between f and the set of unstable functions (with respect to D). We say that a function is stable with respect to D if its spectrum is in D. Here, the notion of spectrum is defined on a case by case basis, as explained below.
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“Free from public debt, at peace with all the world, and with no complicated interests to consult in our intercourse with foreign powers, the present may be hailed as the epoch in our history the most favorable for the settlement of those principles in our domestic policy which shall be best calculated to give stability to our Republic and secure the blessings of freedom to our citizens.”
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