On the stability of fuzzy linear dynamical systems

Abstract

This paper deals with the investigation of the stability of fuzzy linear dynamical systems using the new notion called granular fuzzy Laplace transform. In order to analyzing the stability, some new notions have been introduced such as granular improper fuzzy integral, granular fuzzy Laplace transform, equilibrium points, granular fuzzy transfer function, and etc.. Based on the concept of granular metric, the fuzzy marginal and asymptotic stability of fuzzy dynamical systems are defined. Moreover, using the granular fuzzy Laplace transform, the concept of fuzzy poles and fuzzy zeros are presented. The findings shed light on the advantages and efficiency of the granular fuzzy Laplace transform in comparison with the previous definition of fuzzy Laplace transform. Furthermore, using a theorem proved in this paper we show that the stability of fuzzy linear dynamical systems can also been investigated by a matrix called the granular fuzzy Routh–Hurwitz matrix.