Analyzing stability of haptic interface using linear matrix inequality approach

This paper presents a use of the linear matrix inequality approach to analyze stability of haptic device in the interaction with a virtual wall. The haptic device is modeled as a 1-DoF (Degree of Freedom) linear mechanical system composed of masses, springs and dampers. The virtual wall is modeled as a mechanical system composed of a virtual spring and damper. The paper investigates a discrete-time state-space representation of the haptic system by taken into account the effect of ZOH (Zero Order Holder). The second method of Lyapunov is applied to determine stability boundaries. These boundaries are characterized by the critical virtual stiffness, for several values of delay and virtual damping. The qualitative modification of stable region of the haptic interface under the influence of the flexible mode, the human operator model and the time delay are also presented.