Passivity has been a major criterion on designing a stable haptic interface due to many advantages. However, passivity has been suffering from its intrinsic conservatism since it only represents a small set of the whole stable region. Therefore, there was always limitation to increase the performance due to the small design margin from the passivity criterion. In most of the cases, stability and performance has trade-off relationship. In this thesis, a less conservative control approach is proposed for stable haptic interaction based on Input to State Stable (ISS) criterion. The proposed approach is inspired from the analogy between virtual environments and systems with hysteresis nonlinearities. A system with hysteresis nonlinearity has sector bounded property, which allows us to guarantee that only a finite amount of energy can be extracted from the system, which leads the system to be dissipative  and also the states to be bounded by a function of the input . Since the finite amount of energy is allowed to be extracted from the system, the proposed ISS approach has less conservative constraint compared with passivity-based approaches. Moreover, the proposed approach has a simple structure and does not use any system parameters which make it suitable for practical implementations.
Furthermore, compared with other passivity-based methods, simulation and experiment results show that the proposed approach increases the dynamic range of impedance in which a stable haptic interface can interact.
The presented concept also is extended for stable multi-DOF haptic interaction. In multi-DOF application the concept needs to be applied in each DOF independently to avoid the energy leaking in each DOF. Experimental results show the validity of this concept.
Next, I’ve extended the ISS approach to controllers and teleoperation systems. For the controllers, I’ve proposed a framework to revise the input signal based on the selected output signal to make the system bounded. The presented framework determines the sign of the ISS approach feedback to make the system bounded based on the selected output signal. Then based on the extended frame, I’ve shown how the ISS approach can be applied for different architectures of teleoperation systems. A comparison study with POPC proves that the ISS approach provides more transparent teleoperation. For teleoperation systems with time delay, an observer-based ISS approach is introduced to avoid any energy leaking in the system. The extended idea for teleoperation systems is explained and evaluated experimentally for different teleoperation system architectures with time delay.