On Kharitonov-type results for complex-coefficient interval Schur polynomials

P.P. Vaidyanathan (IEEE Trans. on ASSP, vol.38, no.2, pp. 277-285, Feb. 1990) proposed a new Kharitonov-type result for stability analysis of real Schur polynomials which, after being transformed through a transformation technique, leads to the development of necessary and sufficient conditions for the stability of the transformed polynomials only. In this paper these results are generalized for the complex coefficient case, and it is proven that the stability of eight corner polynomials is both necessary and sufficient for the stability of the whole transformed family of interval polynomials. The sufficiency conditions of this test for the stability of the original interval polynomial family are discussed. The authors elaborate on checking the stability of the required corner polynomials and show how to reduce the number of required polynomials for low-order cases. Some illustrative examples are given. The results may be found useful for testing the interval stability of two-dimensional digital filters