Tradeoffs in Networked Feedback Systems: From Information-Theoretic Measures to Bode-Type Integrals

This paper investigates performance limitation issues of multivariable networked feedback systems with multiport communication channels. We develop a general information-theoretic paradigm for analyzing the limitations and tradeoffs imposed by communication channels, which is enabled by the development of new information measures and Bode-type integral inequalities. The integral inequalities quantify the tradeoffs in disturbance attenuation for broad classes of systems consisting of linear time-invariant plants and causal, possibly nonlinear, time-varying stabilizing controllers communicating over general noisy channels with causal encoders and decoders. The channel blurredness, a newly developed information measure for the quality of multiport communication channels, is used to characterize the effect of communication channel constraints on the integrals and henceforth the tradeoff in disturbance attenuation. For several canonical channels with power constraints, such as additive white Gaussian noise channels, additive colored Gaussian noise channels, and fading channels, we derive explicit forms for the channel blurredness, which, together with the Bode-type integral inequalities, show that to mitigate the noise effect on performance tradeoff, the power of the communication channels must be distributed in ways fundamentally different from the Shannon's classical "water-filling" power allocation policy.