Optimal tracking by LTI controllers over scaled MIMO additive white noise channels

In this paper we study the fundamental limitations in stabilization and tracking of multi-input, multi-output (MIMO) networked feedback systems. We adopt a parallel additive white noise (AWN) model for the MIMO communication channel, and consider as our performance measure the mean square error for a system´s output to track a random reference signal with finite power. Of particular interest in our study is the joint design of the controller and the channel to mitigate the requirement on feedback stabilization and to better the tracking performance. To this effect we consider scaled AWN channels, with positive diagonal scaling matrices interpreted as static coders and decoders. By casting the problem as a constrained optimal H2 control problem and employing duality principles, we derive necessary and sufficient conditions for the system to be mean-square stabilizable and analytical characterizations for the best achievable performance under channel input power constraint. While fundamental limits are known to exist, it is seen that an appropriate channel scaling can be employed to exploit the channel power effectively so as to fundamentally improve a system´s stabilizability and tracking performance.