REDUNDANCE IN APERIODICITY CRITERIA

A previous partial proof of necessary and sufficient conditions for a system to be aperiodic (i.e. to have its characteristic roots all real and simple) is completed in the present paper. Explicit account is taken of the irregular case when the number of Sturm functions is less than the usual number. The number of inequalities in the aperiodicity criteria is n - 1 where n is the degree of the characteristic equation; and for n = 3 it is known that one of the inequalities is redundant. The present investigation shows that redundance does not occur for n ≠ 3. A similar study is made of redundance in criteria for combined aperiodicity and stability. © 1979.