For embedded control systems, a schedule for the allocation of resources to a software component can be described by an infinite word whose $i$th symbol models the resources used at the ith sampling interval. Dependency of performance on schedules can be formally modeled by an automaton (omega-regular language) which captures all the schedules that keep the system within performance requirements. We show how such an automaton is constructed for linear control designs and exponential stability or settling time performance requirements. Then, we explore the use of the automaton for online scheduling and for schedulability analysis. As a case study, we examine how this approach can be applied for the LQG control design. We demonstrate, by examples, that online schedulers can be used to guarantee performance in worst-case condition together with good performance in normal conditions. We also provide examples of schedulability analysis.