Networked stabilization of multi-input systems over MIMO communication

In this paper, we study networked stabilization of a multi-input linear time-invariant (LTI) system closed over a multi-input multi-output (MIMO) communication system modeled as a MIMO transceiver. The controller and encoder/decoder pair are jointly designed subject to a total power constraint. We obtain an analytic solution to the minimum transmission power required for networked stabilization under coding/control co-design given in terms of the topological entropies of cyclic subsystems of the open-loop plant and the quality of service (QoS) of channel eigenmodes of the MIMO channel. Also, an optimal coding/control co-design procedure is proposed. The results generalize the understandings in the literature concerning parallel additive white noise (AWN) channels. A numerical example is provided to verify the results.