Robust stability of interval polynomial sets in discrete-time

Kharitonov (1979) has shown that the robust stability of an interval polynomial, which is the characteristic polynomial in a continuous-time system, can be determined by testing the stability of four polynomials only. In some later results, for the discrete-time counterpart, it was shown that, when realized by the delta operator, for a similar test one needs to test the stability of 2ⁿ⁺¹ polynomials. We present here a novel proof of a similar result in the process of which it is shown that the number of polynomials needed for the test is in fact smaller-this smaller set of polynomials is explicitly specified. Furthermore, we show that as the sampling rate associated with the discrete-time system grows to infinity the stability test presented here converges to the Kharitonov test