A Case Study on Determining Stability Boundaries of Parameter Uncertain Systems

Guaranteeing the stability is one of the fundamental problems of control engineering. In most of the dynamical systems, parameter uncertainties can not be avoided. Thus, it is crucial from a practical point of view to propose generic methods for analyzing the stability of uncertain parameter systems. In this study, the extension of previously proposed Lyapunov Equation based stability mapping approach to the case of parameter uncertain systems is presented. Using the present method, it becomes possible to determine the explicit stability boundaries of the uncertain parameters along with the free controller parameters. Unlike most of the conventional approaches, the current method does not include any restrictions related with the number of the uncertain parameters and the way that the uncertain parameter(s) show themselves in the problem formulation. In order to demonstrate the efficiency of the proposed method, two benchmark case studies are discussed in detail. It is shown that the proposed approach is capable of increasing the accuracy of the previous results in specific cases while ensuring a flexible and easily applicable stability analysis environment for such systems.