An extreme point result for robust stability of discrete-time systems with complex coefficients in two diamonds

For continuous-time systems, the robust stability problem in which the coefficients of the characteristic polynomial vary in a diamond can be considered to be a dual problem to Kharitonov´s theorem on interval polynomials. The aim of this work is to develop similar results for discrete-time systems. Specifically, it has been shown that stability of a family of polynomials with complex coefficients lying in two diamonds of some transformed parameter space can be determined by simply checking twelve extremal polynomials. If the coefficients are real, only four extremal polynomials are required. These results can be viewed as a counterpart of Kharitonov´s result (strong version) for discrete-time systems