Energy-aware control: ℓ2 gain for closed-loop systems implemented with stochastic schedulers

We investigate a control system implemented with a stochastic scheduler on a modern microprocessor where the clock frequency of the microprocessor can be adjusted in real-time. We consider the case when the microprocessor clock frequency may be set so low that the control algorithm occasionally fails to generate an updated control signal in the time allotted to it by the operating system. We seek to understand the relationships between energy consumption, closed-loop performance, and a control signal that is occasionally not updated by the control system. We provide stability and H_∞ performance results for a class of jump linear systems governed by time-inhomogeneous stochastic processes.