Fundamental limitations or performance trade-offs/limits are important properties and constraints of control and filtering systems. Among various trade-off metrics, total information rate, which characterizes the sensitivity trade-offs and average performance of control and filtering systems, is conventionally studied by using the (differential) entropy rate and Kolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutual information -- minimum mean-square error) relationship to the discrete-time additive white Gaussian channels with and without feedback, a new paradigm is introduced to estimate and analyze total information rate as a control and filtering trade-off metric. Under this framework, we enrich the trade-off properties of total information rate for a variety of discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and also provide an alternative approach to investigate total information rate via optimal estimation.

翻译：基础极限或性能权衡/限制是控制与滤波系统的重要特性和约束。在各种权衡指标中，总信息率作为表征控制与滤波系统灵敏度权衡和平均性能的度量，传统上通过（微分）熵率和Kolmogorov-Bode公式进行研究。本文通过将著名的I-MMSE（互信息——最小均方误差）关系扩展到具有和不具有反馈的离散时间加性白高斯信道，引入了一种新的范式来估计和分析作为控制与滤波权衡指标的总信息率。在此框架下，我们丰富了多种离散时间控制与滤波系统（如LTI、LTV和非线性系统）的总信息率权衡特性，并提供了一种通过最优估计研究总信息率的替代方法。