Fuzzy Linear Systems and Stability Analysis

The concept of fuzzy transfer function and fuzzy pole has been proposed here as a way of representing parametric uncertainties in linear models. A fuzzy pole has been introduced in its most general case as a fuzzy complex number represented with a 2-dim membership function. The fuzzy arithmetic needed for required computations has been first studied and a toolbox for MATLAB has been developed to compute fuzzy operations. Using this toolbox, solving system equations and finding the fuzzy poles have been performed in a simple example. Stability analysis of such fuzzy linear systems is then studied as an extension of the classical methods and a new fuzzy nyquist criterion has been proposed. Using these new methods, another concept of stability named possible stability is defined as an alternative for relative stability in particular applications.

Keywords:

Linear system stability analysis , uncertainties and fuzzy systems , fuzzy mathematics