Modelling of uncertain systems using fuzzy numbers

The paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining stability margin of those systems with linear affine dependency of the coefficients of characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of quarter car suspension model.