Stability analysis of fuzzy linear differential equations
Using the concept of credibility measure and the credibility theory founded by Liu [\textit{Baodin Liu}, Uncertainty theory. 2nd ed. Studies in Fuzziness and Soft Computing 154. Berlin: Springer. (2007; Zbl 1141.28001)], the author considers the stability theory for a fuzzy linear differential equation, involving a fuzzy process called the standard Liu process. This formulation involves a new notion of fuzzy differential and fuzzy integral (called Liu integral). The fundamental stability concepts, such as Lyapunov stability, uniform stability, asymptotic stability, uniformly asymptotic stability, global asymtotic stability and stability of exponent \(p\) are introduced for the linear fuzzy Liu differential equation. Some sufficient and necessary conditions for different stability notions of the zero equilibrium point of the linear Liu differential equation are obtained. A few examples are also presented.
scientific article; zbMATH DE number 5719113