Title :
Stability of Fuzzy Differential Equations With the Second Type of Hukuhara Derivative
Author :
Shuorui Zhang ; Jitao Sun
Author_Institution :
Dept. of Math., Tongji Univ., Shanghai, China
Abstract :
In this paper, we consider fuzzy differential equations with the second type of Hukuhara derivative. With the help of Lyapunov-like functions, we establish stability, uniform stability, and uniformly asymptotical stability theorems, respectively, for a class of fuzzy differential equations with the second type of Hukuhara derivative. Besides, a very useful comparison principle is derived, which connects the stability relationships between fuzzy differential equations with the second type of Hukuhara derivative and scalar differential equations. In addition, some examples are shown to illustrate the effectiveness of the results.
Keywords :
Lyapunov methods; asymptotic stability; differential equations; fuzzy set theory; Lyapunov-like functions; fuzzy differential equation stability; scalar differential equations; second type Hukuhara derivative; uniform stability; uniformly asymptotical stability theorems; Asymptotic stability; Differential equations; Equations; Hafnium; Measurement; Stability criteria; Comparison principle; fuzzy differential equations; generalized differentiability; second-type Hukuhara derivative; stability; uniformly asymptotically stable;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2014.2353134
