A New Expression for the Passivity Bound for a Class of Sampled-Data Systems

In this article, we characterize the passivity of a class of haptic systems modeled as a simple sampled-data system. We guarantee passivity by ensuring that there is sufficient damping in the haptic interface. Previous work established a necessary and sufficient bound on damping, but the corresponding mathematical expressions were complicated, and the derivation was not completely rigorous. After providing a rigorous proof, we derive a more tractable expression. Using this improved expression, we establish passivity conditions for several classes of transfer functions representing virtual environments, including some special cases with time delay. The original results assumed that the operator can be modeled by a passive but otherwise arbitrary transfer function. This assumption is weakened to allow the operator model to have a shortage of passivity. This requires only a slight modification of the passivity bound.