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.

کلیدواژه ها:

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