Stable cones of polynomials via Routh rays

A problem of inner convex approximation of a stability domain is addressed in the paper for continuous-time linear control systems. A constructive procedure for generating stable cones of polynomials is provided. The main idea is based on the construction of so-called Routh rays (stable half-lines) starting from a given stable point. These lines serve as edges for the corresponding polyhedral Routh cones inside the stability domain. Several numerical examples are presented to illustrate introduced concepts and effectiveness of the proposed approach.