Abstract: This paper focuses on the problem of H∞ control for linear parameter varying (LPV) discrete time systems with a parameter varying state delay and packet dropouts. The time-delay and state matrix of LPV discrete systems are deterministic functions with parameter variation, the parameter is measurable and constantly changing. Thus, we propose a new H∞ performance criterion depends on the time-varying parameters. The guidelines by introducing an additional matrix eliminates the coupling between Lyapunov functions and system matrices，and it is easier to achieve Value. Under the new condition，the H ∞ state feedback controllers are designed. By using the linear matrix inequality technique, sufficient conditions for the existence of the controller are obtained. Further transformation can obtain the existence condition of the solution of the inequality. Finally, the validity of the method is verified by numerical simulation.

Key words: H∞ control, packet dropouts, discrete time linear parameter-varying systems, linear matrix inequality, state delays

摘要： 研究了一类具有丢包的状态时滞的线性参数变化系统(Linear Parameter-Varying Systems, LPV)离散时间系统的H∞控制问题，此类LPV离散系统的时滞和状态矩阵是随参数变化的确定函数，该参数是可测的且不断变化。基于此，可以给出一种与参数相关的且满足H∞性能指标的准则。此准则具体是通过添加一个附加矩阵，从而解除了原有的系统矩阵与含有参数的Lyapunov函数之间的耦合。在此基础上设计了此类系统的状态反馈控制器，然后，利用线性矩阵不等式技术，求得控制器存在的充分条件，进一步转化可以得到不等式的解存在条件。最后，用实际的例子仿真验证了此方法的有效性。

关键词: H∞控制, 丢包, 离散时间线性参数变化系统, 线性矩阵不等式, 状态时滞