Convex synthesis and limitations of mean-square stabilizing controllers for MIMO systems over packet drop networks

In this paper, we investigate synthesis of linear mean-square stabilizing controllers for multiple-input multiple-output (MIMO) discrete time linear systems over packet drop networks. We consider independent packet drop channels on both the actuator and sensor side of the controller. The main result of this paper is to show that, assuming a delayed acknowledgment from the actuator receiver is available to the controller, a pair of LMI feasibility problems can be used to obtain the mean-square stabilizing controller given fixed channels as well as numerically derive the limitations of mean-square stabilizability in terms of maximal dropout probabilities.