Conservatism of passivity criteria for stability analysis of trilateral haptic systems

Trilateral haptic systems can be modeled as three-port networks. Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. This paper first reviews our recent results in terms of passivity and absolute stability criteria for general three-port networks - both criteria are founded on the properties of a positive-real Hermitian matrix. Next, we show that the absolute stability criterion is less conservative than the passivity criterion and that the two criteria become the same when the trilateral system is represented by a reciprocal immitance matrix. Then, to show how the two criteria may be utilized at the system design stage, we apply them to the problem of designing controllers for a dual-user haptic teleoperation system. Using the two criteria, controllers are then designed and compared in terms of conservatism and performance in simulations.