In this article, we consider the design of an event-triggered ${\ell }_2$-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 ${\ell }_2$-controller for different transmission time-periods with a given ${\ell }_2$-gain bound using the minimax game-theoretical approach. After that, we propose an ${\ell }_2$-consistent event-triggered controller in the sense that it guarantees at least the same ${\ell }_2$-gain bound as the designed periodic time-triggered ${\ell }_2$-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.

在本文中，我们考虑事件触发的设计 ${\ell }_2$控制策略，用于调度程序正在仲裁从离散时间线性系统的传感器到控制器的状态传输的设置。我们首先介绍一个定期的时间触发${\ell }_2$给定的不同传输时间控制器 ${\ell }_2$-使用minimax博弈论方法获得收益。之后，我们建议 ${\ell }_2$-一致的事件触发控制器，从某种意义上说，它保证至少相同 ${\ell }_2$-增益为设计的定期时间触发 ${\ell }_2$-控制器，但是具有更大或最多等于的平均间传输时间。在实践中，与典型的干扰相比，建议的事件触发方案与定期的时间触发策略相比，可以在通信节省和干扰衰减方面带来显着收益。