Convergence analysis of tele-operation systems with unsymmetric time-varying delays

This note addresses the stability problem of tele-operation system with unsymmetric time-varying delays. The human operator contains a constant force on the master robot, thus the passive condition is not satisfied. The master and the slave sites are coupled using PD control strategy. By choosing new Lyapunov Krasovskii functional, we show that the master-slave tele-operation system is asymptotically stable under specific LMI conditions. With the given PD (Proportional-Derivative) parameters, we can obtain the allowable maximum delay values. Finally, simulations are performed to show the effectiveness of the proposed method.