Self-triggered stabilization of homogeneous control systems

Digital implementations of feedback laws commonly consider periodic execution of control tasks. In this paper we go beyond the periodic model by developing self-triggered schedules for the execution of control tasks. These schedules guarantee asymptotic stability under sample-and-hold implementations while drastically reducing processor usage when compared with the more traditional periodic implementations. At the technical level the results rely on a homogeneity assumption on the continuous dynamics and extend to the self-triggered framework some of the advantages of event-triggered implementations recently studied by the authors. The results presented in this paper can be seen as an effort towards understanding the real-time scheduling requirements of control tasks.