Abstract: The stability of discrete-time linear system with two delays and application to network control system are discussed.A discrete-time linear system with state delay，when its signal of the state gets out from system to controller，there are two cases.The first one is that it has two channels，one is input into controller directly，the other is transmitted via network，time-delay caused by network transmission.The second one is that it has single-channel via network.Based on Lyapunov stability theory，a sufficient condition to guarantee the system with two delays stabilization is obtained.By introducing some new variables，the derived condition is formulated in terms of Linear Matrix Inequalities（LMIs） so that the controller for two cases is easily obtained.Finally，three examples are given to illustrate the developed results.

Key words: discrete-time system, stability, network control, time-delay

摘要： 研究了具有双时滞离散线性系统的稳定性及其在网络控制中的应用。一个具有状态时滞的离散线性系统，假设它的状态信号从输出到控制器的时候，存在两种情况：第一种情况，有两条传播渠道，一条直接输入到控制器，另一条通过网络，网络传播往往会产生时滞；第二种情况是通过网络单渠道传送。基于Lyapunov稳定理论得到双时滞离散线性系统稳定的充分条件。在此基础上通过引入一些新的变量，将得到的条件转化为线性矩阵不等式（LMIs），分别给出了两种情况下控制器的设计。最后给出的三个数值例子说明方法的有效性。

关键词: 离散系统, 稳定性, 网络控制, 时滞