Stability and passivity of feedback interconnected systems in network environments

This paper investigates stability and passivity of negative feedback interconnection of two passive systems, which are interconnected through communication networks. The insertion of communication networks between negative feedback interconnected passive systems inevitably induces delays and data packet dropouts. To model the network-based negative feedback interconnected system, an appropriate network scheduling method is presented to deal with time-varying network-induced delays and data packet dropouts. By constructing a novel discontinuous Lyapunov-Krasovskii functional, a less conservative sufficient condition for the network-based feedback interconnected system to be asymptotically stable is derived. Based on the stability condition, a new sufficient condition to make the negative feedback interconnected system in network environments remain passive is developed. A numerical example is provided to demonstrate the effectiveness of the design method.