Stability analysis of event-triggered networked control systems with time-varying delay

Networked control systems(NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control (ETC) is often used to reduce the amount of communications while still keeping a satisfactory performance of the system, by transmitting the state measurements only when an event-triggered condition is met. However, some network-induced problems would happen inevitably, such as communication delay. The delay can degrade the control performance significantly and can even lead to instability. In this paper, we study an NCS considering both ETC and time-varying delay, which is rare in the literature. We formulate the system as a discretized piecewise linear system with exponential uncertainty. Then the model is embedded in a polytopic approximation with better structure suitable for stability analysis. Stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, the developed method is illustrated by a numerical example.