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
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=4183)
denotes the nominal point,
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1629)
denotes the space of all possible values of the object
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2038)
, and the shaded area,
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2412)
, represents the set of points that satisfy the stability conditions.