An ℓ₂-consistent event-triggered control policy for linear systems

In this article, we consider the design of an event-triggered ℓ₂-control policy, for a setting where a scheduler is arbitrating state transmissions from the sensors to the controller of a discrete-time linear system. We start by introducing a periodic time-triggered ℓ₂-controller for different transmission time-periods with a given ℓ₂-gain bound using the minimax game-theoretical approach. After that, we propose an ℓ₂-consistent event-triggered controller in the sense that it guarantees at least the same ℓ₂-gain bound as the designed periodic time-triggered ℓ₂-controller, however with a larger, or at most equal, average inter-transmission time. In practice, for typical disturbances, the proposed event-triggered scheme can lead to significant gains, both in terms of communication savings and disturbance attenuation, compared to periodic time-triggered policies, which is illustrated through a numerical example.