Generation of stable polytopes of Hurwitz polynomials via Routh parameters

The paper addresses an important issue in the field of continuous-time linear control systems - convex stability domain approximation problem. The constructive procedure of generating a stable polytope is proposed. The main idea is based on constructing so-called Routh stable line segments (half-lines) starting from a given stable polynomial. It is summarized in the form of a step-by-step algorithm that results in a stable polytope around a given point. Several numerical examples are presented to demonstrate the covered concepts and the effectiveness of the proposed approach. Calculations are performed in a MATLAB environment.