An LMI framework for analysis and design of multi-dimensional haptic systems

This paper presents a convenient framework based on passivity and linear matrix inequalities (LMIs) for stability analysis and controller design for haptic systems involving multiple devices and human operators interacting with a common virtual environment. The proposed approach addresses peculiar features of the multi-dimensional scenario such as different operator-device configurations, and allows for taking into account structural constraints such as decentralized controller implementation. An LMI-based stability condition is given and a a class of stabilizing structured controllers that can be parameterized in terms of the solution of suitable LMI problems is introduced.