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

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.