Robust Stability of a Class of Unstable Systems under Mixed Uncertainty

For unstable plants, the priority of control goes to the stability of synthesis, which means to find a stabilizer controller. In the case where the plant is subjected to structured and unstructured uncertainties, the stability problem becomes more crucial. The problem was solved by a conservative method based on generalized Kharitonov's theorem and Nevanlinna-Pick's interpolation (NPI) technique. This paper introduces a proposed straightforward numerical approach for loop shaping the unstructured additive or multiplicative maximum uncertainty magnitudes. The approach finds controllers, which are capable of stabilizing the interval system while the uncertainty box is enlarged to its maximum dimensions. To illustrate, we introduce some numerical examples.