Convex synthesis and limitations of mean-square stabilizing controllers for MIMO systems with actuator-side dropouts

In this paper we investigate synthesis of linear control producing mean-square stability of a multiple-input multiple-output (MIMO) discrete time linear system having communication channels in the loop on the actuation side. We consider a quite general plant and assume the communication channels are subject to dropout with known probabilities. We provide numerically tractable methods to design mean-square stabilizing controllers for such scenarios and analyze the limitations as a function of channel variances. The main result of the paper is to show that the design of state feedback and output feedback with delayed channel state information available at the controller are convex problems by providing equivalent linear matrix inequality (LMI) feasibility problems.