Computation of Stability Regions using Boundary Locus and Kronecker Summation Methods

In this paper the computation of all stabilizing PI controllers for third order systems are obtained using Boundary locus and Kronecker summation method. Stabilizing PI controllers in the (k(p),k(i)) plane guarantees the stability of a feedback system. The Kronecker summation method needs the explicit equation in terms of controller parameters that defining the stability boundary in parameter space. The explicit expression needs the characteristic equation. Using this explicit expression, auxiliary characteristic equation is formulated using Kronecker summation operation. This auxiliary characteristic equation defines the stability boundary. The stabilizing region obtained using this method is compared with boundary locus method. The third order systems are considered to show the effectiveness of these methods and are simulated using Matlab.