Stabilization Over Power-Constrained Parallel Gaussian Channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of
H
₂
control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoders.