On Feedback Passivity of Discrete-Time Nonlinear Networked Control Systems With Packet Drops

We analyze the feedback passivity of a networked control system in which the control packets may be dropped by the communication channel. Specifically, we consider a discrete-time switched nonlinear system with relative degree zero that switches between two modes. At the instants when the communication link transmits the packet successfully, the system evolves in closed-loop and the increase in storage function is bounded below the energy supplied by the control input. At the instants when a packet drop occurs, the system evolves in open loop according to the free dynamics of the closed-loop mode and the increase in storage function is not necessarily bounded by the supplied energy. The literature on passivity of switched systems seems to consider only the case when all the modes are passive, which is not the case here. We prove that if the ratio of time steps for which the system evolves in closed-loop versus in open loop is lower bounded by a critical number, the system is locally feedback passive in a suitably defined sense. This generalized definition of feedback passivity is useful since it preserves two important properties of classical passivity—that feedback passivity implies asymptotic stabilizability for zero state detectable systems and that feedback passivity is preserved in parallel and negative feedback interconnections.