Passivity results for interconnected systems with time delay

It is well known that a negative feedback interconnection of passive systems is passive. However, the extension of this fundamental property to the case when there are time delays in communication, remains largely unaddressed. In this paper we demonstrate that a negative feedback interconnection of output strictly passive systems, under appropriate assumptions, is passive for non-increasing time delays and may loose passivity for increasing time delays. Passivity can be retained by inserting time-varying gains in the communication path, provided a bound on the maximum rate of change of delay is known. If the dynamical systems are passive, we appeal to the results in bilateral teleoperation, to recover passivity of the feedback interconnection.We show that by transforming the two systems into their scattering representation, transmitting the scattering variables as the new outputs, and using time-varying gains in the communication path, passivity of the feedback interconnection can be guaranteed independent of the time-varying delays. Finally we discuss the applicability of the proposed results for networked control of nonlinear mechanical systems.