Control over Signal-to-Noise Ratio Constrained Channels: Stabilization and Performance

Previous papers have considered the problem of using linear time invariant control to stabilize an unstable plant over a signal-to-noise ratio constrained communication channel, and have shown that this problem reduces to one of minimizing the H2norm of the complementary sensitivity function. Different techniques were used to derive the state and output feedback results, and it is not straightforward to characterize the performance that is achieved when output feedback is used with a nonminimum phase plant. In the present paper, a unified treatment of the state and output feedback cases is obtained by posing the problem as one of LQG optimal control. Doing so allows us both to analyze the achieved performance, in terms of sensitivity reduction, as well as to incorporate performance into the problem statement. When performance is considered, the results have interpretations in terms of Wiener filtering.