Fuzzy Lyapunov stability and exponential stability in control ‎systems‎

Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case of which is exponential stability) and input-output stability. This paper develops fuzzy Lyapunov stability through investigating the concept of stability for finite-dimensional systems under uncertainty and provides some related theorems. Considering the capability of fuzzy differential systems for modeling uncertainty and processing vague or subjective information in mathematical models, exponential stability and Lyapunov stability of fuzzy differential systems are presented. Also, numerical examples are given to support the theoretical ‎results.