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-offreedom haptic interface—is given and discussed in some detail.  1997 John Wiley & Sons, Inc.