Computation of Stability Regions for Third Order Systems using Boundary Locus and Kronecker Summation Methods

This paper deals with the design of continuous time robustly stabilizing Proportional-Integral(PI) controllers for interval plants using the Boundary locus method and Kronecker summation method. Stabilizing PI controllers in (k(p),k(i)) plane guarantees the stability of a feedback system. Boundary locus method is based on plotting the stability boundary locus in the (k(p),k(i)) plane and then computing the stabilizing values the parameters of a PI controller. Kronecker summation method needs the explicit equation in terms of control parameters that defines the stability boundary in parameter space. The explicit equation needs the characteristic equation. Using the explicit equation, auxiliary characteristic equation is formulated using Kronecker summation operation This auxiliary characteristic equation defines the stability boundary. Furthermore, these methods are used to compute all the parameters of a PI controller which stabilize a control system with an interval plant family. The third order interval systems are considered to show the effectiveness of these methods and are simulated using matlab.