Stability radius

The stability radius of an object (system, function, matrix, parameter) at a given nominal point is the radius of the largest ball, centered at the nominal point, all of whose elements satisfy pre-determined stability conditions. The picture of this intuitive notion is this:

where ${\displaystyle {\hat {p}}}$ denotes the nominal point, ${\displaystyle P}$ denotes the space of all possible values of the object ${\displaystyle p}$, and the shaded area, ${\displaystyle P(s)}$, represents the set of points that satisfy the stability conditions. The radius of the blue circle, shown in red, is the stability radius.

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