In this article, we study the -stability in qth moment (.s.q.m) of hybrid neutral stochastic differential equations with infinite delay (HNSDEID) using Lyapunov techniques and method M-matrix. Finally, apply main result to some examples.

<p style='text-indent:20px;'>This paper is concerned with stablization of hybrid differential equations by intermittent control based on delay observations. By M-matrix theory and strategy, we establish a sufficient stability criterion stochastic equations. Meantime, show that can be stabilized observations if the time <inline-formula><tex-math id="M1">\begin{document}$ \tau $...