H∞ state-feedback control of bilateral teleoperation systems with asymmetric time-varying delays

In this study, a novel controller synthesis method is proposed for the bilateral teleoperation systems with asymmetric time-varying delays. The main idea of the proposed method is to deal with the control problem for a bilateral teleoperation system under asymmetric time-varying delays as a control problem for a system with multiple input time delays, and then to find the state-feedback control law to stabilise the system with guaranteed H-infinity performance on the defined control output. With intentionally introducing the pretend time delays to the (local) state variables of the master or the slave, the teleoperation controller design problem is converted to a controller synthesis problem for a system with multiple input time delays. Then the state-feedback controllers are designed for both the master and the slave by defining an appropriate Lyapunov-Krasovskii functional candidate and solving linear matrix inequalities. The designed controllers guarantee the closed-loop system stability and system transparency performance in terms of the optimised H-infinity norm on the position and force tracking errors between the master and the slave. At last numerical simulations are used to validate the effectiveness of the proposed method. The results show that the designed controllers can effectively stabilise the present teleoperation system with good transparency performance under time-varying delays.