Fundamental limitations or performance trade-offs/limits are important properties and constraints of both control and filtering systems. Among various trade-off metrics, total information rate that characterizes the sensitivity trade-offs and time-averaged performance of control and filtering systems was 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) relationships 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 explore the trade-off properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.

翻译：基本性能极限或性能权衡/极限是控制系统与滤波系统的重要属性与约束。在众多权衡指标中，表征控制系统与滤波系统灵敏度权衡及时间平均性能的总信息率，传统上通过微分熵率与柯尔莫哥洛夫-博德公式进行研究。本文通过将著名的I-MMSE（互信息-最小均方误差）关系推广至含反馈与不含反馈的离散时间加性高斯白噪声信道，引入了一种新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，我们探索了各类离散时间控制与滤波系统（如LTI、LTV及非线性系统）总信息率的权衡特性，并提出了一种通过最优估计研究总信息率的替代方法。