Exponential stability of neutral stochastic differential functional equations with Markovian switching

A sufficient condition of exponential stability is established for a class of neutral stochastic differential functional equations Markovian jumping parameters. The analysis consist in using Burkholder-Davis-Gundy lemma and Ito's formula derived for our stability purposes. The stability results derived also are applied to a piecewise deterministic system which arises quite often in practice in systems with multiple modes. An application to neutral stochastic differential functional equation is studied to illustrate our theory.