Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability.

Lyapunov stability theory provides a powerful technique for stability analysis of dynamical systems, particularly for the stability of nonlinear dynamical system. This paper deals with the stability of fuzzy dynamical systems using a novel notion called granular fuzzy Lyapunov function. In order to analyze the stability, some new notions are introduced such as fuzzy equilibrium point, the ball of fuzzy state space, granular fuzzy 2-norm and etc. Based on the concept of fuzzy-number-valued function granular differentiability, two theorems are proved for calculation. Moreover, using granular fuzzy Lyapunov function, the granular fuzzy local stability theorem is proposed, and two definitions of exponential stability and like-Lyapunov stability are generalized. Finally, several examples are given to illustrate the proposed theorems. • The granular fuzzy chain rules and granular fuzzy 2-norm are presented. • Granular fuzzy Lyapunov function based on fuzzy-number-valued function granular derivative was defined. • The local stability theorem stability is proposed, and two definitions of exponential stability and like-Lyapunov are generalized. [ABSTRACT FROM AUTHOR]