Determination of vertex polynomials to analyse robust stability of control systems with interval parameters

The study describes the application of the root locus theory for a system whose characteristic polynomial has interval coefficients. For the proposed system, an interval extension of the basic angular equation of the root locus is performed. Upon the conditions for defining the robust oscillatory stability degree through a complex pole of the system, the double interval angular inequations are obtained. These inequations specify the range of the exit angles going out of the poles for all edge branches of the root locus. On the basis of the exit angles of edge branches going out of the real pole, the condition for determining the robust aperiodic stability degree is obtained. Moreover, an algorithm for finding the validation vertices of the polyhedron of coefficients is developed and some sets of vertex polynomials for low-order systems are specified. The study also presents some numerical examples for analysing the robust stability degree in interval systems, which confirm our theoretical results. It is concluded that the determined validation vertices provide an optimal solution to the analysis of robust stability.