Stability of discrete-time linear system with two delays and application to network control system

The stability of discrete-time linear system with two delays and application to network control system is discussed. For a discrete-time linear system with state delay, there exists two channels from which signal of the state transmit from system to controller. One is input into controller directly, the other is transmitted via network. Network transmission usually generates time delay, then the close-loop system can be regarded as a discrete-time linear system with two delays. Based on Lyapunov stability theory, a sufficient condition to guarantee the system stabilization is obtained. By introducing some new variables, the derived stability condition is formulated in terms of linear matrix inequalities (LMIs) and their solutions provide a representation of the controller. Finally, two examples are given to illustrate the developed results.