Co-design between robust L1 fault-tolerant control and discrete event-triggered communication scheme for networked control systems with transmission delay and quantisation

In order to take into account both the system performance and economical utilisation of network resources, under the discrete event-triggered communication scheme, the problems of the robust $L_{1} $L1 fault-tolerant control for a class of uncertain networked control systems with actuator fault constraint are investigated. In consideration with the imperfect networked environment with transmission delay and quantisation, a model of the error dependent networked closed-loop fault system is established. By constructing an appropriate delay-dependent Lyapunov–Krasovskii functional, the sufficient condition for the existence of robust $L_{1} $L1 fault-tolerant controller is obtained for an error dependent networked closed-loop fault system, and a co-design method for gaining the discrete event-triggered parameter and $L_{1} $L1 fault-tolerant controller is proposed in terms of linear matrix inequalities. Notice that the structure of Lyapunov–Krasovskii functional which considers the piecewise-linear sawtooth structure characteristic of transmission delay, a less conservative result is obtained. Finally, simulation examples are provided to illustrate the feasibility of the proposed method.