The presence of uncertam parameters an a state space or frequency domain description of a linear, time-invariant system manifesis itself as varmbility in the coefficients of the characteristic polynomial. If the famity of all such poly. Nomials is polytodic in coefficient space, we show that the root locations of the entife tamily can be completely determined by examinine only the roots of the porynomuals contained in the exposed edges of the polyiope These proccdutes are compotationally tractabie and this cnterion inipiores upon the prescntly avaitabic stabity tests for uncertain systems. being less ed acvative and explicitly deler. munmg at root locations Equally important is in laci that the results are also applicable to discrete-time systems