Linear Fuzzy Delay Differential System: Analysis on Stability of Steady State

Abstract

In this paper, a first order linear fuzzy delay differential system is proposed by using parametric form of alpha-cut representation of symmetric triangular fuzzy number. The steady state and linear stability of the system are also determined. The steady state is stable in absence of delay by Routh-Hurwitz criteria. For increasing delay we determine the positive real roots of the polynomial and developing the conditions. Several examples are considered to illustrate the stability of the steady state for the proposed system. Keywords: Delay Differential Equations; Fuzzy Differential Equations; Fuzzy Matrices. 2010 Mathematics Subject Classification: 34K36.