User-friendly MATLAB program for control and robust stability analysis of systems with parametric uncertainties

Abstract

The paper describes a user-friendly package for continuous-time control and robust stability analysis of SISO systems affected by parametric uncertainties. Concretely, the specific and common case of the closed-loop system containing controlled system with interval parameters is supposed. The program has been created in the MATLAB+Simulink environment with the support of Polynomial Toolbox. The implemented algebraic method of control design is based on general solutions of linear Diophantine equations in the ring of proper and Hurwitz stable rational functions (R-PS), conditions of divisibility and the Youla-Kucera parameterization of controllers. Moreover, a scalar positive parameter is introduced for tuning and influencing of control behaviour. Robust stability is investigated through the value set concept, zero exclusion condition and Kharitonov theorem.