This paperis on the application of information theory to the analysis of fundamental lower bounds on the maximum deviations in feedback control systems, where the plant  is linear time-invariant while the controller can generically be any causal functions as long as it stabilizes the plant. It is seen in general that the lower bounds are characterized by the unstable poles (or nonminimum-phase zeros) of the plant as well as the conditional entropy of the disturbance. Such bounds provide fundamental limits on how short the distribution tails in control systems can be made by feedback .
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic \mathcal{L where the plant (i.e., the dynamical system to be controlled) is linear time-invariant , and it is seen in general that the lower bounds are characterized by the unstable poles (or nonminimum-phase zeros) of the plant as well as the conditional entropy of the disturbance. We then analyze the setting where the plant is assumed to be (strictly) causal, for which case the lower bounds are determined by the conditional entropy of the disturbance. We also discuss the special cases of p = 2 and p = \infty, which correspond to minimum-variance control and controlling the maximum deviations, respectively. In addition, we investigate the power-spectral characterization of the lower bounds as well as its relation to the Kolmogorov-Szeg\"o formula .
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This paperis on the application of information theory to the analysis of fundamental lower bounds on the maximum deviations in feedback control systems,
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic \mathcal{L
A
(i.e., the dynamical system to be controlled)
R
while the controller can generically be any causal functions as long as it stabilizes the plant. It
, and it
R
Such bounds provide fundamental limits on how short the distribution tails in control systems can be made by feedback
We then analyze the setting where the plant is assumed to be (strictly) causal, for which case the lower bounds are determined by the conditional entropy of the disturbance. We also discuss the special cases of p = 2 and p = \infty, which correspond to minimum-variance control and controlling the maximum deviations, respectively. In addition, we investigate the power-spectral characterization of the lower bounds as well as its relation to the Kolmogorov-Szeg\"o formula