H2 controller design of networked bilateral teleoperation system with Markovian time delays

This paper studies the stability and the H
₂
controller design of bilateral teleoperation systems with symmetric random communication delays whose stochastic variation is modeled as a Markov chain. The error dynamics of the bilateral teleoperation system are derived by considering the user and environment forces as disturbances. The Markovian property of the time delays is incorporated into the error dynamics and controllers corresponding to the different delays are proposed to improve the tracking performance. The necessary and sufficient conditions for the stochastic stability of the bilateral teleoperation system with the proposed controllers are derived. Lastly, the H
₂
optimal controller design method is proposed in terms of solving a set of linear matrix inequalities (LMIs). The theoretical analysis is validated through simulation results.