LQ-based event-triggered controller co-design for saturated linear systems

This paper deals with the simultaneous design of a state feedback law and an event-triggering condition ensuring local exponential stability and LQ performance in the presence of plant input saturation and of a communication channel between the controller output and the saturated plant input. To this aim, we adopt Lyapunov-based techniques in a hybrid framework. The design of the event-triggered control is based on two conditions: one to solve the event-triggered control co-design for LQ stabilization; the second one to adjust the co-design among all possible solutions of the first condition thanks to a tunable parameter. The proposed Lyapunov formulation yields an event-triggered algorithm to update the saturated plant input based on conditions involving the closed-loop state, while an estimate of the domain of attraction is provided. Furthermore, a trade-off is highlighted relating the optimality level, the size of the estimate of the basin of attraction and the reduction of the amount of transmissions.