Delay and data packet dropout separately related stability and state feedback stabilisation of networked control systems

There exist bounded transmission delay and data packet dropout in the networked control systems (NCSs). When the sensors and actuators are time-driven and controllers are event-driven, the NCSs can be modelled as a class of discrete-time systems with time-varying input delay. Most of similar articles simply combine delay and packet dropout to analyse and synthesise NCSs without distinguishing their different impacts, which leads to conservative results. In this study, the authors summarise that the number of consecutive data packet dropout increases gradually in case of packet dropout. A novel Lyapunov-Krasovskii functional is constructed based on this increment property, so less conservative results are obtained through the Lyapunov-Krasovskii functional approach. In addition, the upper bound of a Lyapunov functional difference cross term is reasonably estimated to further reduce the conservativeness. Stability and stabilisation criteria which are separately related to the transmission delay and data packet dropout are presented. The obtained conditions are based on linear matrix inequalities, which can be solved easily by MATLAB or other numerical software.