Análise comparada da estabilidade robusta na perspectiva determinística e estocástica.

Abstract

This work presents a methodology based on classical statistics principles with a view to determining the regions of robust stability of linear or non-linear systems, with a reduced level of conservatism relative to deterministic methods. The random nature of the roots of the characteristics equation of the system represented by their probability distributions is with regard to the universe of all possible outcomes for the phenomenon. This means that it is possible to map the roots by using the statistical distance as a metric associated with the chi-squared function to a level of significance α. Thus, the roots can be collected, thereby generating the probability distributions. In addition, the region in the complex plane that contains them is thereby established. One of the problems of deterministic methodology lies in not considering interactions between variables and another problem is the so-called "inverse problem". Within the scope of deterministic analysis, it is observed that such an analysis considers the roots of the characteristic equation are distributed uniformly. Comparisons with the classical methods of analysis of stability such as the root-locus, the concept of bounded input/bounded output and Lyapunov stability theory, are also included in the analysis made in this article. Such comparisons have indicated that the results obtained using the methodology presented are less conservative, and therefore producing an analysis and mapping of robustness of stability more realistically, because it considers all variables, parameters and simultaneous interactions between them, without the need to assess the individual contributions of each variable, related to stability analysis. The proposed method also allows a check on the stability region to be run continuously, thus assessing its tendency, and therefore determining the need for decision-making, in a timely manner, in order to restore such a region. In work is used a reactive system and other non-reactive system, in order to evaluate the behavior of the methodology and it is effects.