Maximum Stability Controller Synthesis for a System with an Interval Characteristic Polynomial Using Critical Root Diagrams

This article considers the application of critical root diagrams for the synthesis of a maximum stability robust controller. These diagrams describe the root arrangement variants where the maximum stability degree is achieved in stationary systems. The article solves the problem of providing the maximum stability degree for the one-parameter controller. This regulator is used in the system with interval-indefinite coefficients of the characteristic polynomial. For this, algebraic conditions are obtained. Under these conditions, the stability degree will be maximum. Also, the algorithm of regulator synthesis is given. Based on these conditions and algorithms, the limiting stability degree of the third-order interval system is found.