Design constraints and limits of networked feedback in disturbance attenuation: An information-theoretic analysis

In this paper we investigate the intrinsic design constraints and performance limits of networked control systems. We propose new information measures and correspondingly, develop an information-theoretic paradigm for analyzing the performance trade-offs and limits in disturbance attenuation over information-constrained networked feedback, which is enabled by a cohesive development of new information measures, Bode-type integral inequalities, and performance bounds. The integrals and bounds incorporate the information measures and serve to quantify the trade-offs and limits in disturbance attenuation for broad classes of networked feedback 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 notion of negentropy rate is introduced to address general, non-Gaussian disturbances. The channel blurredness, a newly proposed information measure for the quality of communication channels, is used to characterize the effect of communication channel noises on the integrals and henceforth the trade-offs in disturbance attenuation. Bounds on the power gain, a novel disturbance attenuation measure tailored for performance analysis of networked control systems, provide the fundamental limits of disturbance attenuation achievable by networked feedback.