On self-triggered control for linear systems: Guarantees and complexity

Typical digital implementations of feedback controllers periodically measure the state, compute the control law, and update the actuators. Although periodicity simplifies the analysis and implementation, it results in a conservative usage of resources. In this paper we drop the periodicity assumption in favor of self-trigger strategies that decide when to measure the state, execute the controller, and update the actuators according to the current state of the system. In particular, we develop a general procedure leading to self-triggered implementations of feedback controllers, that highly reduces the number of controller executions while guaranteeing a desired level of performance. We also analyze the inherent trade-off between the computational resources required for the self-triggered implementation and the resulting performance. The theoretical results are applied to a physical example to show the benefits of the approach.