Passivity of a class of sampled-data systems: Application to haptic interfaces

Passivity of systems comprising a continuous time plant and discrete time controller is considered. This topic is motivated by stability considerations arising in the control of robots and force-reflecting human interfaces (“haptic interfaces”). Necessary conditions for passivity are found via a small gain condition, and sufficient conditions are found via an application of Parseval's theorem and a sequence of frequency domain manipulations. An example—implementation of a “virtual wall” via a one degree-of-freedom haptic interface—is given and discussed in some detail.