Abstract
The robustness of a control system is concerned with the ability of such a system to keep the characteristics of stability and performance when subjected to disturbances and uncertainties in the parameters, or in plants with unknown dynamics. The analysis of robustness enables an assessment to be made of whether the desired performance of the control system is maintained even when there are changes in the process, thus making such systems insensitive to such changes, and consequently, allowing robust control systems to be designed which may be able to meet the requirements of the project. Successful analysis of a control system, particularly the analysis of stability, may involve both deterministic and statistical treatments. However, if deterministic techniques are used as if the systems were deterministic, such an approach can have severe implications and lead to misleading results or at least, yield substantially conservative results. While the approach with statistical techniques may not always reduce the uncertainties, this can, however, lead to more precise statements thus enabling better decisions to be made. Since the system under study is considered stochastic by nature, this paper is devoted to assessing the robustness of stability by statistical methods whereby the confidence region for each root of the characteristic equation can be established. Such a technique considers as a metric the statistical distance which is associated with the chi-square distribution, thus permitting the quadratic form to be established, as well the contour of the resulting ellipse, which thus reveals the robustness sought.
