On simplified Hurwitz stability conditions for low-degree weighted diamond polynomials

In this paper, the results on the stability of a weighted diamond of polynomials which was studied by Kharitonov and Tempo (Systems Control Lett. 22 (1994)) are simplified for low-order polynomials. Specifically, for n=3 and 4, the number of polynomials required to check the stability is four and six, respectively, instead of eight. Further, diamond of polynomials which were studied by Barmish et al. (IEEE Trans. Automat. Control AC-37 (9) (1992)) are also investigated.