Some discrete-time counterparts to extreme point results for robust stability of a diamond of polynomials

The main result of the paper is that a family of polynomials with roughly half of all the real coefficients lying in a diamond is robustly Schur stable if and only if all the extreme polynomials are Schur stable. This special polynomial family is called a degenerate diamond of polynomials. In addition, we obtain the extreme point result for robust Schur stability of a so-called simplex degenerate diamond polynomial family.