Bode-like integral for stochastic switched systems in the presence of limited information

In this paper, we establish a Bode sensitivity integral formula for a class of feedback closed-loop systems with stochastic switched plants and controllers. Using information theory, we study the information conservation law, based on which a log integral theorem is obtained for the closed loops of interest. Furthermore we develop several algebraic conditions to explicitly capture the performance limitations. Application of this theoretical framework to Networked Control Systems (NCS) is used as an illustrative example.