H∞ and L1 control of a teleoperation system via LMIs

This paper presents a new linear matrix inequality approach to robust H∞ and L1 controllers design for a bilateral teleoperation system. The time delay of communication media is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known. In this approach, an impedance controller is designed for the master side and an open-loop controller is designed for the slave side. Also, an optimal disturbance rejection technique is developed for the slave side. In order to design the slave side controller, the control system is reformulated such that the slave side controller is converted to an equivalent dynamic output feedback controller in a standard control system representation. A Lyapunov–Krasovskii functional is defined for stability analysis. The main results provide sufficient delay-dependent conditions for the stability analysis and control design problem. The criteria are expressed as a set of linear matrix inequalities, which can be easily examined using standard numerical software.