Control over Additive White Gaussian Noise Channels: Bode-Type Integrals, Channel Blurredness, Negentropy Rate, and Beyond ?

This paper aims at developing Bode-type integrals for control systems over additive white Gaussian noise channels, by way of deriving information theoretic equalities and inequalities. The integrals characterize the fundamental performance trade-offs of such networked feedback systems with linear time-invariant plants and causal stabilizing controllers. We propose two new notions to facilitate our development: channel blurredness and negentropy rate. The channel blurredness provides an alternative measure for the quality of communication channels to the conventional notion of channel capacity. The negentropy rate, on the other hand, relates the entropy rate of a stochastic process to its power spectrum. Both notions are shown to be closely relevant to networked feedback systems. Indeed, the Bode-type integrals developed herein are seen to depend on the channel blurredness of the communication channel, as well as the negentropy of the exogenous disturbances.