Previous researches on analysis of stability of haptic simulation largely assume that the virtual environment is passive. But the virtual environment can become non-passive due to various reasons including discretization errors and interaction dynamics between virtual tools and objects. This paper provides an analysis of the stability and performance of the haptic simulation involving non-passive virtual environment. The dynamic interaction between the virtual tools and the objects is modeled using the two-port networks. The analysis is carried out using a velocity and force mapping matrix for six-DOF simulation. New stability condition resulting from the analysis is applied to an example simulation of a one-DOF virtual wall. Maximum stiffness satisfying the stability condition established in the previous literature, and the proposed condition is compared with the maximum stiffness experimentally determined with various time steps. The newly proposed stability condition manifests less standard deviation of errors than the widely applied absolute stability condition.

The possibility of operating in remote environments using teleoperation systems has been considered widely in the control literature. This paper presents a review on the discrete-time teleoperation systems, including issues such as stability, passivity and time delays. Using discrete-time methods for a master-slave teleoperation system can simplify control implementation. Varieties of control schemes have been proposed for these systems and major concerns such as passivity, stability and transparency have been studied. Recently, unreliable communication networks affected by packet loss and variable transmission delays have been received much attention. Thus, it is worth considering discrete-time theories for bilateral teleoperation architectures, which are formulated on the same lines as the continuous-time systems. Despite the extensive amount of researches concerning continuous-time teleoperation systems, only a few papers have been published on the analysis and controller design for discrete bilateral forms. This paper takes into account the challenges for the discrete structure of bilateral teleoperation systems and notifies the recent contributions in this area. The effect of sampling time on the stability-transparency trade-off and the task performance is taken into consideration in this review. These studies can help to design guidelines to have better transparency and stable teleoperation systems.

In order to better understand the dynamics of acute leukemia, and in particular to findtheoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia,we investigate stability of a system modeling its cell dynamics.

The overall system is a cascade connection of sub-systems consisting of distributeddelays and static nonlinear feedbacks. Earlier results on local asymptotic stability areimproved by the analysis of the linearized system around the positive equilibrium. For thenonlinear system, we derive stability conditions by using Popov, circle and nonlinearsmall gain criteria. The results are illustrated with numerical examples andsimulations.

An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators under consideration contains many standard hysteresis nonlinearities which are important in control engineering such as backlash (or play), plastic-elastic (or stop) and Prandtl operators. Whilst the main results are developed in the context of integral equations of convolution type, applications to well-posed state space systems are also considered.

We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.