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

Matt Rich and Nicola Elia

To appear in: 53rd IEEE Conference on Decision and Control (CDC) December 2014

In this paper, we investigate synthesis of linear mean-square stabilizing control 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. We provide an efficient, numerically tractable methodology to design meansquare stabilizing output feedback control requiring delayed acknowledgment from the plant which achieves the same limitations as state feedback, and to analyze the design limitations as a function of channel dropout probabilities. The main result of this paper is to show that synthesis of such output feedback control as well as the analysis of the limitations is a convex problem by providing an equivalent linear matrix inequality (LMI) feasibility problem.