Analysis of Systems with Parametric Uncertainty Described by Fuzzy Functions

In the paper an interesting application of fuzzy approach is presented. The problem of stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. Each coefficient is considered as a variable interval parametrized by the degree of confidence in validity of the corresponding model. The higher the confidence level is the smaller is the interval in which the corresponding coefficient can lie. Here the common confidence level for all the coefficients is taken into account. The confidence level is interpreted as a membership degree of a fuzzy set: if the confidence level is equal to 1 (the maximum value) the crisp linear system (or system with minimum coefficient variation) is considered; if the confidence level is equal to 0 (the minimum value) an interval linear system is taken into account with maximum admissible interval for each coefficient. In this way we can model linear systems with variable interval uncertainty parametrized by the confidence level, parameter which can be estimated. In this paper triangular fuzzy sets for each coefficient are supposed.