Bode-like Integral for Continuous-Time Closed-Loop Systems in the Presence of Limited Information

Abstract

This paper analyzes causal closed-loop continuous-time systems in the presence of limited information. Assuming that the exogenous signals can be modeled as a stochastic process, a mutual information rate inequality is obtained that can be viewed as an extended Bode-type formula for stationary processes. The tightness of the resulting Bode's integral inequality is then analyzed for the linear time invariant closed loops. Within the developed framework we consider the control-communication interplay and analyze the underlying fundamental limitations.