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

A Kharitonov-type result for the stability analysis of real Schur polynomials that have been transformed by a new transformation technique has been proposed, and the necessary and sufficient conditions for the stability of the transformed polynomials were developed by P.P. Vaidyanathan (see IEEE Trans. Acoust. Speech Signal Process, vol.38, no.2, p.277-85, 1990). These results are generalized to the case of the complex coefficient, and the stability of the whole transformed family of interval polynomials is proved. The sufficiency conditions of this test for the stability of the original interval polynomial family is commented on, and checking the stability of the required polynomials for low-order cases is addressed. Some illustrative examples are given. The results may be found useful to testing the interval stability of two-dimensional digital filters