Stable digital control networks for continuous passive plants subject to delays and data dropouts

This paper provides a framework to synthesize l²- stable networks in which the controller and plant can be subject to delays and data dropouts. This framework can be applied to control systems which use "soft-real-time" cooperative schedulers as well as those which use wired and wireless network feedback. The approach applies to passive plants and controllers that can be either linear, nonlinear, and (or) time-varying. This framework is based on fundamental results presented here related to passive control and scattering theory which are used to design passive force-feedback telemanipulation systems. Theorem 3 states how a (non)linear (strictly input or strictly output) passive plant can be transformed to a discrete (strictly input) passive plant using a particular digital sampling and hold scheme. Furthermore, theorem 4(5) provide new sufficient conditions for l² (and L²)-stability in which a strictly - output passive controller and plant are interconnected with only wave-variables. Lemma 2 shows it is sufficient to use discrete wave-variables when data is subject to fixed time delays and dropouts in order to maintain passivity. Lemma 3 shows how to safely handle time varying discrete wave-variable data in order to maintain passivity. We then present a new cooperative scheduler algorithm to implement a I²-stable control network. We also provide an illustrative simulated example followed by a discussion of future research.