Finite-time $H_{\infty}$ control for stochastic Markov jump systems with uncertainty

This article discusses a class of finite-time
$H_{\infty}$
control problem for linear stochastic systems with uncertainty and external disturbances. First, the definitions of finite-time stochastic stability and boundedness for linear stochastic systems with uncertainty are given. Then, state feedback controller is designed with the linear matrix inequalities, such that the closed-loop systems satisfy the
$H_{\infty}$
performance conditions, and sufficient conditions for the existence of controllers are presented. Finally, an example is given to show that the state feedback controllers designed in this article are effective.