Stabilization of hybrid stochastic systems with time-varying delay by discrete-time state feedback control

In this paper, we are concerned with the stabilization of hybrid stochastic systems with variable delay by discrete-time state feedback control. By using Lyapunov functionals, we obtain an upper bound τ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau ^{*}$\end{document} on the duration τ between two consecutive state observations. Meantime, we show that hybrid stochastic systems with variable delay can be stabilized by discrete-time state feedback control as long as τ<τ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau <\tau ^{*}$\end{document}. Finally, two examples are given to demonstrate the applicability of our work.