Trade-offs in information-limited feedback systems: MIMO Bode-type integrals and power allocation

In this paper we study Bode-type integrals for multivariate networked feedback systems in which the uplink and downlink noisy channels are present simultaneously. The integrals, which are obtained via an information-theoretic approach, characterize explicitly the fundamental performance trade-offs of disturbance attenuation in networked control systems. Two information-theoretic measures, termed negentropy rate and channel blurredness respectively, are proposed to quantify the effect of the multivariate disturbance and communication channel constraints on the Bode-type integrals. In particular, when it comes to parallel additive white Gaussian noise channels, channel blurredness leads to a totally new `fire-quenching´ power allocation policy in contrast to the conventional `water-filling´ solution.