Stabilization of MIMO systems over additive correlated noise channels subject to multiple SNR-constraints

This paper studies the mean square stabilization of MIMO discrete-time linear time-invariant systems over a MIMO additive correlated channel. We assume that such channel consists of multiple correlated SISO channels subject to independent input signal-to-noise ratio (SNR) constraints. We derive explicit conditions for which mean square stabilization can be achieved under such constraints for unstable minimum phase plants, and characterize the controller that achieves such SNR. We also present the set of admissible SNR constraints for mean square stability for a particular set of plants. Our results show that noise correlation can reduce the SNR requirements for stability compared to independent additive white noise channels. In addition, a numerical simulation is provided to illustrate the theoretical results.