Synthesis of sampling modes of multi-rate systems for guaranteed stability

Adaptive regulation of sampling period has gained significant attention in research community in recent times and some encouraging techniques has been reported in this research direction. One such promising technique is commonly referred as multi-rate sampling. A linear control system that uses multi-rate sampling contains a collection of sampling periods and appropriately designed controllers for the corresponding sampling modes. Further, the switching between the sampling modes may depend upon some switching guards. In this paper, we address the problem of the multi-rate sampling associated with linear time invariant control systems, by formalizing the basis of selecting the sampling periods for the different sampling modes, such that overall system stability under arbitrary switching can be guaranteed. We also present a framework for controller synthesis in a multi-rate setting, such that our primary goal is achieved. Further, we present a case study using standard academic example and provide results in support of our proposed methodology.