Aperiodicity and periodicity of interval polynomials

Three 'Kharitonov-like regions' for the root location of interval polynomials are indicated. The regions are the imaginary axis, the open left half of the real axis, and the open right half of the real axis. Polynomials whose roots all lie in the open left half real axis are called aperiodic and those with roots only on the imaginary axis, periodic. It is shown that for aperiodicity or periodicity of interval polynomials, checking of the property of only two extreme polynomials is sufficient. Furthermore, the results obtained recover the original Kharitonov theorem. That is, they can provide an alternative way to prove Kharitonov's theorem.<>