Stability analysis of fuzzy systems (Q5926829)

The paper considers the stability of systems described by fuzzy relational equations, i.e. of systems where the inputs, the states and the outputs are linguistic variables described by linguistic values that are mapped into fuzzy sets. To achieve a practical stability criterion, the concept of a bounded linguistic variable is introduced. It is proposed that the universe of discourse of the linguistic variable consists of two parts, the stable and the unstable parts. Using these two regions and after giving some basic definitions, a new stability concept is introduced. Further, using this new concept, two well-known stability criteria (the energetic stability and the equilibrium stability) are modified to achieve practical applicability. Several illustrative examples are included.