Stabilization of MIMO Systems Over Multiple Independent and Memoryless Fading Noisy Channels

This paper investigates the state feedback stabilizability problem for multi-input multi-output systems over memoryless fading noisy channels under stationary signal-to-noise ratio constraints. The channel is modeled as a cascade of a multiplicative noise and an additive white Gaussian noise. The aim of the addressed problem is to find the minimum overall quality of service required to render the stabilization possible. The essential idea of our approach is to view the stabilization from the perspective of a demand/supply balance. Specifically, each control input is considered as the demand side for communication resource while the channels are considered as the supply side. The supply resource of the channels is characterized by their respective quality of service. The stabilization of the networked systems requires the demand/supply balance of the communication resource. Depending on whether the channel resource is configurable or not, two different approaches are adopted for realizing the required balance. If the channel resource is configurable, one can tailor the supply to meet the demand via channel resource allocation; otherwise, one can shape the demand to meet the supply via certain transceivers design mechanism. Explicit conditions on the minimum overall quality of service for networked stabilization are established in both scenarios.