Exponential stability and stabilization of linear multi-rate sampled-data systems

This paper addresses stability analysis and controller synthesis for linear multi-rate sampled-data systems. In these systems, a plant with linear dynamics is controlled by a linear controller which is located in the feedback loop between a sensing block and a zero-order-hold. The sensing block comprises several sensors with asynchronous uncertain non-uniform sampling intervals. We present sufficient Krasovskii-based stability and stabilization criteria as a set of linear matrix inequalities. It is shown through examples that choosing the right sensors with adequate sampling frequencies has a considerable impact on controller design and stability of the closed-loop system.