Exponential stability of fuzzy differential equations (Q2458996)

The author provides sufficient conditions for the exponential stability of the trivial solution of the following fuzzy differential equation \[ \frac{dx}{dt}=f(t,x), \;x(t_{0})=x_{0}, \] where \(f\in C(\mathbb R_{+}\times S(\rho), E^{n}) \) is a given fuzzy function, \ \(S(\rho)=\{x\in E^{n}: d(x,\hat 0)<\rho\}\) and \(E^{n}\) is the set of fuzzy numbers. The results are obtained by means of appropriate Liapunov functions.