On Passivity of Networked Nonlinear Systems with Packet Drops

We analyze passivity for a class of discrete-time switched nonlinear systems that switch between two modes an uncontrolled mode in which the system evolves open loop, and a controlled mode in which a control input is applied to the system. Such a model has recently been used for a network controlled system in the presence of packet drops introduced by a communication channel. For the case when the open loop system is non-passive, classical passivity theory considers the switched system to be non-passive as well. We give a new generalized definition of passivity for such a system and show that if the ratio of the time steps for which the system evolves open loop versus the time steps for which the system evolves closed loop is bounded below a critical ratio, then the nonlinear system is locally passive in this sense. Moreover, we show that this generalized definition is useful since it preserves two important properties of the classical passivity concept that passivity implies asymptotic stability for zero state detectable systems using feedback and that passivity is preserved in parallel and feedback interconnections.