$H_{\infty}$ Control of Delayed Teleoperation Systems under Polytopic-Type Uncertainties

Abstract

International audienceIn this paper, the $H_{\infty}$ control design under time-varying delays and polytopic-type uncertainties, which ensures the stability and performance (synchronization/transparency) between the master and slave manipulators, is proposed. With this objective, the design of the controller based on our proposed control scheme is performed by using Linear Matrix Inequality (LMI) optimization based on Lyapunov-Krasovskii functionals (LKF) and $H_{\infty}$ control theory. The solution is efficient for different working conditions, \emph{e.g.} abrupt tracking and wall contact motion, and this is illustrated by a final example