Determination of the Region of Stabilizing Controller Parameters of Polytopic Polynomials

Abstract

In the scenario of robust controller design for any given MIMO process system, control-designer faces real challenges in computing the optimum region of controller-parameters by following the conventional methodologies. Such methods are, in fact, much complex for analyzing and hence time consuming. In this paper, we employ the method of Kharitonov’s Theorem to determine the region for stabilizing controller-parameters (of polytypic polynomials). The main advantage of using this method is that it can be adopted or not only SISO, but also for MIMO system of any order; even if having perturbations in them. The Generalized Kharitonov Theorem given here provides a constructive solution to this problem by reducing it to the Hurwitz stability of a prescribed set of extremal line segments. The number of line segments in this test set is independent of the dimension of the parameter space. This test set has many important extremal properties that are useful in control systems