This paper considers the finite-time $H_{\mathrm{\infty }}$ control problem for Markovian jump systems (MJSs) with time-varying delay and generally uncertain transition rates (GUTRs). Based on Lyapunov-Krasovskii functionals and free-weight matrices, some sufficient conditions for finite-time boundedness and $H_{\mathrm{\infty }}$ finite-time boundedness of MJSs are derived in the presence of external disturbances and It$\hat{o}$-type stochastic disturbances. A state feedback controller is proposed to achieve $H_{\mathrm{\infty }}$ finite-time boundedness performance. By applying linear matrix inequalities (LMIs), the parameterisation of the controller is converted to a convex optimisation problem. Finally, a practical example demonstrates the effectiveness of the proposed method.

本文考虑有限时间 $H_{\mathrm{\infty }}$具有时变延迟和一般不确定的转换率 (GUTR) 的马尔可夫跳跃系统 (MJS) 的控制问题。基于 Lyapunov-Krasovskii 泛函和自由权矩阵，有限时间有界的一些充分条件和$H_{\mathrm{\infty }}$ MJSs 的有限时间有界是在存在外部干扰的情况下推导出来的，它$\widehat{○}$型随机扰动。提出了一种状态反馈控制器来实现$H_{\mathrm{\infty }}$有限时间有界性能。通过应用线性矩阵不等式 (LMI)，控制器的参数化转换为凸优化问题。最后，一个实际例子证明了所提出方法的有效性。