Passivity and L2 stability of networked dissipative systems

It is well known that a negative feedback interconnection of passive systems is passive. However, the extension of this fundamental property to the case of negative feedback interconnection of dissipative systems, which is a more general case, remains largely unaddressed. In this paper, we demonstrate that a negative feedback interconnection of dissipative systems, under appropriate assumptions, could be passive or just L2 stable; we further propose a way to relax these assumptions. The case when there are time delays in communication is then addressed, and it is shown that under appropriate assumptions, the closed-loop system is passive or L2 stable for non-increasing time delays; moreover, passivity and L2 stability 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.