Maximizing the stability radius of a set of systems under real-time scheduling constraints

We address the problem of synthesising real-time embedded controllers taking into account constraints deriving from the implementation platform. Assuming a time-triggered model of computation for tasks controlling a set of independent systems and a real-time preemptive scheduling policy managing a single CPU processor board, we deal with two problems: 1- deciding whether a performance specification can be met on a given platform, 2- optimising performance on a platform. Decision variables of the design problems are the activation periods of the tasks , while the considered performance metric is the minimum stability radius attained over the different feedback loops, which is related to the technological feasibility of the controller and to the robustness of the controlled systems. The analytical formulation of the design problems enables efficient numerical solutions. The resulting control policies are directly implementable without performance degradation that may otherwise arise due to scheduling and execution delays.