Entropy and Stability in Fuzzy Control Systems-A Theoretical Analysis

This paper studies the theoretical relationship between entropy and stability in fuzzy control systems. Fuzzy entropy is employed to measure the uncertainty or fuzziness in the system and its influence on unstable behaviour of systems. Accomplishing this through mathematics formulations and derivations, we prove that fuzzy control systems of lower entropy are more stable. This document is authenticated by a well-known practical example related to the temperature regulation system in which we calculate entropy values and determine stability using Lyapunov's direct method. This indicates that the reduction of entropy is critical to improving the stability and reliability in fuzzy control systems. This study brings a new guideline for stability analysis and suggests useful thoughts to design the higher stable fuzzy systems.