Stability analysis of fuzzy systems

An important issue in control theory is stability. Even though fuzzy control has been successfully applied to many control problems, the issue of system stability has not been resolved. We show that stability criteria developed so far for fuzzy systems described by fuzzy relational equations have no practical application. To achieve a practical stability criterion we introduce the concept of a bounded linguistic variable. We augment the universe of discourse of a linguistic variable by defining stable and unstable regions. Then, after giving a few basic definitions, we give a new stability theorem and apply it to assess stability of a non-linear fuel engine. The same concept of a bounded linguistic variable is also used to enhance the energetic stability criterion and the equilibrium point stability criterion and make them suitable for practical applications.