Control Over a Packet Dropping Network with Norm Bounded Uncertainties

In this paper, we consider a robust networked control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller as well as between the controller and plant. We investigate the effect of data drop out in the form of packet losses and we focus on the tradeoff between packet arrival rate versus the uncertainties of the system dynamics. We show that the minimum packet arrival rate and the maximum uncertainty of the system dynamics have a positive correlation. Four distinct control schemes are explored and serve as examples to study this tradeoff. We derive sufficient condition for each scheme to ensure almost sure stability of the closed loop system. Simulation and examples are provided to assist the theory.