LMI stability constraints for disjoint stability regions using rouché theorem

Stability domain characterization in coefficients space of polynomials is considered. Generalization of existing results on convex approximation of stability domain in coefficients space is proposed. The proposed method can handle broad class of stability regions including unions of disjoint stability regions. New LMI formulation of stability constraints is developed for discrete-time polynomials. Numerical examples are provided, demonstrating the applicability of the proposed method.