This paper provides a sufficient 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 framework applies to plants and
controllers which are passive, therefore these passive systems can
be either linear, nonlinear, and (or) time-varying. This framework
arises from fundamental results related to passive control, and
scattering theory which are used to design passive force-feedback
telemanipulation systems, in which we provide a short review.
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. Based
on these new theories, we provide an extensive set of new results
as they relate to LTI systems. For example, Proposition 2 shows
how a LTI strictly-output passive observer can be implemented. We
then present a new cooperative scheduler algorithm to implement
an l2-stable control network. We also provide an illustrative
simulated example which uses a passive observer followed with
a discussion for future research.