Event-triggered control with LQ optimality guarantees for saturated linear systems

Given a predesigned linear state feedback law for a linear plant ensuring (global) exponential stability of the linear closed loop, together with a certain level of performance, we address the problem of recovering (local or global) exponential stability and 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 which combine generalized sector conditions to deal with the saturation nonlinearity, and event-triggered techniques to deal with the communication channel. The arising analysis yields an event-triggered algorithm to update the saturated plant-input based on conditions involving the closed-loop state. The proposed Lyapunov formulation leads to numerically tractable conditions that guarantee local (or global) exponential stability of the origin of the sampled-data system with an estimate of the domain of attraction.